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פרופ' צבי ארד

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Papers presented:
1)       On the p-solvability of finite groups containing certain Hall subgroups (joint research with D. Chillag).
2)      On maximal subgroups with a nilpotent subgroup of index (joint research with M. Herzog and A. Shaki).
Papers presented:
1)            On Frobenius problem (joint research with D. Chillag and M. Herzog).
2)            On products of conjugacy classes in groups (joint research with J. Stavi and M. Herzog).
 
Papers presented:
1)  On products of conjugacy classes and irreducible characters in finite groups.
2)  On products of irreducible characters and conjugacy classes of finite groups in complementary sets.
 
List of Publications
Books
1A.         Products of Conjugacy Classes in Groups, Lecture Notes in Mathematics, Springer-Verlag (Editors: Z. Arad and M. Herzog), vol. 1112, 1985, 244 pp.              
1B.          Homogeneous Integral Table Algebras of Degree Three: A Trilogy, (with H. Blau, Bangteng Xu, E. Fisman, V. Miloslavsky and M. Muzychuk), A.M.S. Mem., vol. 144, no. 684, March 2000.
1C.          Standard Integral Table Algebras Generated by a Non-real Element of Small Degree (Editors: Z. Arad and M. Muzychuk), Lecture Notes in Mathematics, Springer, vol. 1773, 2002.
1D.         Ischia Group Theory 2004 in honour of Marcel Herzog (Editors: Z. Arad, W.Herfort, M. G. Bianchi, P. Longobardi, M. Maj, C. Scoppola), Contemporary Mathematics vol. 402, Israel Mathematical Conference Proceedings, American Mathematical Society, 2006.
1E.          On Normalized Integral Table Algebras (Fusion Rings) Generated by a Faithful Non- real Element of Degree 3 (Principal author Zvi Arad jointed with Xu Bangteng, Guiyan Chen, Effi Cohen, Arisha Haj Ihja Hussam  and Mikail Muzychuk (accepted), ~300 pages. Springer - Verlag Series : Algebra and applications, Vol.16,2011, 274PP.
 
Articles
2.            Products of Fitting classes of finite groups, Israel J. of Math. 12, No. 1 (1972), 61-69.
3.            p-homogeneity and p-closure of finite groups, Pacific J. of Math. 51 (1974), 1-9.
4.       A characteristic subgroup of p–stable groups, Canadian J. of Math. 6 (1974), 1509-1514.
5.            Groups with s2'-subgroups and s3'-subgroups, Israel J. of Math. 17, no. 1 (1974), 76-83.
6.            A characteristic subgroup of a group of odd order (with G. Glauberman), Pacific J. of Math. 56 (1975), 305-319.
7.            p-closure of finite p-solvable groups, J. Australian Math. Soc. 21 (1976), 118-119.
8.            Abelian and nilpotent subgroups of maximal order of groups of odd order, Pacific J. of Math. 62 (1976), 29-35.
9.            A classification of 3 cc groups and applications to Glauberman-Schmidt theorem, J. of Algebra 42 (1976), 176-180.
10.          A classification of groups with a centralizer condition, Bull of the Australian Math. Soc. 15 (1976), 81-85.
11.          A classification of groups with a centralizer condition (with M. Herzog), Bull. of the Australian Math. Soc. 16 (1977), 55-60.
12.          On finite groups containing a cc-subgroup (with D. Chillag), Arch. der Math. 29 (1977), 225-234.
13.          On fundamental subgroups of order divisible by three (with M. Herzog), Houston J. of Math. 3 (1977), 309-313.
14.          A classification of groups with a centralizer condition II: Corrigendum and addendum (with M. Herzog), Bull. Australian Math. Soc. 17 (1977).
15.          On finite groups with conditions on the centralizers of p-elements (with D. Chillag), J. of Algebra 51 (1978), 164-172.
16.          On a theorem of N. Ito on factorizable groups (with D. Chillag), Arch. der Math. 30 (1978), 236-239.
17.          Injectors of finite solvable groups (with D. Chillag), Comm. in Algebra 7(2), (1979), 115-138.
18.          On centralizers of elements of odd order in finite groups (with D. Chillag), J. of Algebra 61 (1979), 269-280.
19.          Finite groups with conditions on the centralizers of p-elements (with D. Chillag), Comm. in Algebra 7 (14), (1979), 1447-1468.
20.          On finite groups containing three cc-subgroups (with P. Feguson), Proc. A.M.S. 80 (1980), 27-33.
21.          p-solvability and nilpotent Hall subgroups (with D. Chillag), Proc. of Symposia in Pure Math. 37 (1980), 197-199.
22.          On finite groups with almost nilpotent maximal subgroups (with M. Herzog, and A. Shaki), J. of Algebra 65 (1980), 445-452.
23.     On a property like Sylow’s of some finite groups (with D. Chillag), Arch. der Math. 35 (1980), 401-405.
24.          On maximal subgroups with a nilpotent subgroup of index 2 (with M. Herzog, and A. Shaki), Proc. of Symposia in Pure Math. 37 (1980), 201-203.
25.          Classification of finite groups by a maximal subgroup (with M. Herzog, and D. Chillag), J. of Algebra 71 (1981), 235-244.
26.          Finite groups containing a nilpotent Hall subgroup of even order (with D. Chillag), Houston, J. of Math. 7 (1981), 23-32.
27.          On a problem of Frobenius (with M. Herzog and D. Chillag), J. of Algebra 74 (1982), 516-523.
28.          A classification of locally finite and profinite groups with a centralizer condition (with W. Herfort), Comm. in Algebra 10 (16), (1982), 1749-1764.
29.          New criteria for solvability of finite groups (with M. Ward), J. of Algebra 77 (1982), 234-246.
30.          A criterion for the existence of normal p-complements in finite groups (with D. Chillag), J. of Algebra 87 (1984). 472-482.
31.          On finite factorizable groups (with E. Fisman), J. of Algebra 86 (1984), 522-548.
32.          On solvability of finite groups (with M. Ward), Arch. der Math. 42 (1984), 489-491.
33.          Survey on products of conjugacy classes in groups (with M. Herzog), Proceedings of the Fourth International Conference on Representations of Algebras, Carleton-Ottawa Mathematical Lecture Notes Series 2 (1984), 2.01-2.04.
34.          Groups with a small covering number (with D. Chillag and G. Moran), Lecture Notes in Math., Springer-Verlag 1112 (1985), 222-244.
35.          Powers and products of conjugacy classes in groups (with M. Herzog and J. Stavi), Lecture Notes in Math., Springer-Verlag 1112 (1985), 6-51.
36.          Powers of characters of finite groups (with D. Chillag and M. Herzog), J. of Algebra 103 (1986), 241-255.
37.          On products of irreducible characters and conjugacy classes of finite groups in complementary sets (with E. Fisman), A.M.S. Lecture Notes, prepared in connection with the Summer Institute on Representations of Finite Groups, (1986), S5-ZA/EF-1-26.
38.          On products of conjugacy classes and irreducible characters in finite groups, A.M.S Lecture Notes, prepared in connection with the Summer Institute on Representations of Finite Groups, (1986), S6-ZA-1-12.
39.          An analogy between products of two conjugacy classes and products of two irreducible characters in finite groups (with E. Fisman), Proc. of the Edinburgh Math. Soc. 30 (1987), 7-22.
40.          On products of irreducible characters and conjugacy classes of finite groups in complementary sets (with E. Fisman), Proceedings of Symposia in Pure Math. 47 (1987), 11-23.
41.          On products of conjugacy classes and irreducible characters in finite groups, Proc. of Symposia in Pure Math. 47 (1987), 3-9.
42.          A proof of Szep’s conjecture on nonsimplicity of certain finite groups (with E. Fisman), J. of Algebra 108 (1987), 340-354.
43.          Table algebras and applications to finite group theory, Proc. of I.M.U., Tel-Aviv University, 1987.
44.          On products of irreducible characters and products of conjugacy classes in finite groups (with E. Fisman), J. of Algebra 114 (1988), 466-476.
45.          Determination of finite groups by certain subgroups and a solution to Szep’s conjecture, Periodica Mathematica Hungaria 19 (1988), 175-179.
46.          A note on a finite subset of a group closed under multiplication of distinct elements (with J. Lennox) Arch. der Math. 50 (1988), 300-301.
47.          On products of characters in finite groups (with H. Lipman), Houston J. of Math. 15 (1989), 305-326.
48.          Survey on table algebras and applications to finite groups theory, Israel Math. Conf. Proc. , vol. 1 (1989), 96-110.
49.          An application of Ramsey’s theory to partitions in groups. I (with G. Ehrlich, O.H. Kegel and J. Lennox), Rendiconti del Seminario Matematico della Universita di Padova 84 (1990), 143-157.
50.          An infinite family of nonabelian simple table algebras not induced by finite nonabelian simple groups (with H. Blau), Proc. of Groups – St. Andrews 1989, Cambridge University Press, Lecture Notes Series 159 (1991), 29-37.
51.          Table algebras and applications to products of characters in finite groups (with H. Blau and E. Fisman), J. of Algebra 138 (1991), 186-194.
52.          On table algebras and applications to finite groups theory (with H. Blau), J. of Algebra 138 (1991), 137-185.
53.          On table algebras, C-algebras and applications to finite group theory (with E. Fisman), Comm. in Algebra 19(11), (1991), 2955-3009.
54.          An application of Ramsey’s theory to free products of partitions of groups II (with G. Ehrlich and O.H. Kegel), Rendiconti del Seminario Matematico della Universita di Padova 89 (1993), 57-81.
55.          Zeros in character tables of finite groups, Algebra Colloquium 1 (1994), 225-232.
56.          Real table algebras and applications to finite groups of extended Camina-Frobenius type (with H. Blau, J. Erez and E. Fisman), J. of Algebra 168 (1994), 615-647.
57.          Table algebras of extended Gagola type and applications to finite group theory (with E. Fisman and C. Scoppola), Groups’93, Galway/St. Andrews, London Math. Soc. Lect. Notes Series 211, vol. 1 (1995), 13-22.
58.          The structure of metabelian finite groups (with E. Fisman and M. Muzychuk), Groups ’93, Galway/St. Andrews, London Math. Soc. Lect. Notes Series 211, vol. 1 (1995), 6-12.
59.          Order evaluation of products of subsets in finite groups and its applications, I (with E. Fisman and M. Muzychuk), J. of Algebra 182 (1996), 577-603.
60.          Order evaluation of products of subsets in finite groups, II (with M. Muzychuk), Transactions of the A.M.S., vol. 349, 11, 750 (1997), 4401-4414.
61.          Order evaluation of products of subsets in finite groups and its applications for the estimation of the covering number of conjugacy classes (with M. Muzychuk), In “Semigroups” (Kar Ping Shum, Yugi Guo, Masami Ito, Yuen Fong, eds.), Springer Verlag (1998), 11-16.
62.          On a product of two elements in a non-commutative C-algebras (with  E. Fisman and M. Muzychuk), Algebra Colloquium 5:1 (1998), 85-97.
63.          Homogeneous integral table algebras of degree two, three and four with a faithful element, Proceedings of Groups St. Andrews 1997 in Bath, I, L.M.S. Lecture Note Series 260 (1999), 20-29.
64.          Generalized table algebras (with E. Fisman and M. Muzychuk), Israel J. of Math. 114 (1999), 29-60.
65.          On antisymmetric homogeneous integral table algebras of degree 3 (with E. Fisman, V. Miloslavsky and M. Muzychuk), Mem. of the A.M.S., vol. 144, No.684, March 2000.
66.          Integral table algebras with a faithful nonreal element of degree three, (with E. Fisman, A. Husam and M. Muzychuk), J. of Algebra 231 (2000), 463-472.
67.          Integral table algebras with a faithful nonreal element of degree four (with E. Fisman, H. Arisha, and M. Muzychuk), Chapter 2 in the book: Standard Integral Table Algebras Generated by a Non-real Element of Small Degree, (Z. Arad and M. Muzychuk, eds.), Lecture Notes in Mathematics, Springer, vol. 1773, 2002.
68.          Standard integral table algebras with a faithful non-real element of degree five (with F. Bunger, E. Fisman and M. Muzychuk), Chapter 3 in the book: Standard Integral Table Algebras Generated by a Non-real Element of Small Degree, (Z. Arad and M. Muzychuk, eds.), Lecture Notes in Mathematics, Springer, vol. 1773, 2002.
69.          On even GT–algebras (with Y. Erez and M. Muzychuk), J. of Algebraic Combinatorics 17 (2003), 163-170.
70.          Connections between degrees and other table algebra constants and applications for finite groups (with Y. Erez and M. Muzychuk), J. of Applied Algebra and Discrete Structures 1 (1) (2003), 35-78.
71.          (Pro)-finite and (topologically) locally finite groups with a CC-subgroup (with W. Herfort), London Math. Soc. Lecture Note Series 304, Groups St. Andrews 2001 in Oxford, vol 1, Cambridge Univ. Press (2003), 6-11.
72.          Table algebras generated by elements of small degrees (with M. Muzychuk), London Math. Soc. Lecture Note Series 304, Groups St. Andrews 2001 in Oxford, vol 1, Cambridge Univ. Press (2003), 12-21.
73.          On normalized table algebras generated by a faithful non-real element of degree 3   (with G. Chen), Advances in Algebra; Proc. of the ICN Satellite Conf. in Algebra and Related Topics, ed. K.P. Shum, World Scientific Pub., Dec. (2003), 13-37.
74.          Classification of finite groups with a CC-subgroup (with H. Wolfgang), Comm. in Algebra 32 (2004), 2087-2098.
75.          On standard integral table algebras generated by an element of width 2 (with M. Muzychuk and Y. Erez), Israel J. of Math. 142 (2004), 285 -314.
76.          Finite groups with distinct sizes of conjugacy classes (with M. Muzychuk and A. Oliver), J. of Algebra 280 (2004), 537-576.
77.         Topologically locally finite groups with a cc-subgroup (with W. Herfort), J. Lie Theory 815 (2005), 235-248.
78.         On normalized table algebras generated by a faithful non-real element of degree 3 (with Guiyun Chen), J. of Algebra 283 (2005), 457-484.
79.         Maximal cyclic subgroups and prime divisors in finite simple groups (with W. Herfort), Arch.der Math. 85 (2005), 31-36.
80.          Homogeneous integral table algebras of degree four (with Y. Erez and M. Muzychuk), Comm. in Algebra 34 (2006), 463-519.
81.          The history of the classification of finite groups with a CC-subgroup (with W. Herfort), Contemporary Mathematics, Israel Mathematics Conference Proc., American Mathematical Society, vol. 402 (2006), 1-11.
82.          Classification of table algebras with two basis elements whose product is a linear combination of their conjugates (with E. Cohen), Algebra Colloquium 13, no.4 (2006) 569-599.
83.          On normalized table algebras generated by a faithful non-real element of degree 3, II (with Guiyun Chen and H. Arisha), Cornell University Library, arxiv.org (www.arxiv.org), (2008), 170 pages.
84.          Special decompositions of products in table algebras (with E. Cohen), Algebra Colloquium 16, no.1 (2009), 1-16.
85.          On non- solvable  Camina pairs (with M. Muzychuk, A.Mann and C. Pech),
                J.of Algebra 322, no. 7 (2009), 2286-2296
86.          On normalized integral table algebras (Fusion Rings) generated by a faithful non–real element of degree 3 – Chapter 1 (Zvi Arad and Effi Choen) Springer-Verlng Series: Algebra and applications Vol.16, 2011.
87.          On normalized integral table algebras (Fusion Rings) generated by frithful non-real element of degree 3- Chapter 2 (with G.Chen and H.Arisha),Springer Verlag Series: Algebra and Applications, Vol.16, 2011.
88.          On normalized integral table algebras (Fusion Rings) generated by a faithful non–real element of degree 3 – Chapter 3 (with Xu Bangteng), Spring – Verlag Series: Algebra and applications Vol.16, 2011.
89.          On normalized integral table algebras (Fusion Rings) generated by a faithful non–real element of degree 3 – Chapter 4 (with E. Cohen),
         Springer-Verlag Series: Algebra and applications, Vol 16,2011.
90.          On normalized integral table algebras (Fusion Rings) generated by a faithful non–real element of degree 3 - Chapters 5 (with E. Cohen and M. Muzychuk),
          Springer-Verlag Series : Algebra and applications, Vol 16,2011.
 
 
 
 

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