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http://dx.doi.org/10.4134/CKMS.c180086

NON-REAL GROUPS WITH EXACTLY TWO CONJUGACY CLASSES OF THE SAME SIZE  

Robati, Sajjad Mahmood (Department of Mathematics Faculty of Science Imam Khomeini International University)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.1, 2019 , pp. 137-143 More about this Journal
Abstract
In this paper, we show that $A_4$ is the only finite group with exactly two conjugacy classes of the same size having some non-real linear characters.
Keywords
conjugacy classes; irreducible characters; solvable groups;
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1 Y. Berkovich, Finite solvable groups in which only two nonlinear irreducible characters have equal degrees, J. Algebra 184 (1996), no. 2, 584-603.   DOI
2 Y. Berkovich and L. Kazarin, Finite nonsolvable groups in which only two nonlinear irreducible characters have equal degrees, J. Algebra 184 (1996), no. 2, 538-560.   DOI
3 Ya. G. Berkovich and E. M. Zhmud, Characters of Finite Groups. Part 1, translated from the Russian manuscript by P. Shumyatsky [P. V. Shumyatskii] and V. Zobina, Translations of Mathematical Monographs, 172, American Mathematical Society, Providence, RI, 1998.
4 M. Bianchi, A. G. B. Mauri, M. Herzog, G. Qian, and W. Shi, Characterization of non-nilpotent groups with two irreducible character degrees, J. Algebra 284 (2005), no. 1, 326-332.   DOI
5 C. M. Boner and M. B. Ward, Finite groups with exactly two conjugacy classes of the same order, Rocky Mountain J. Math. 31 (2001), no. 2, 401-416.   DOI
6 D. Chillag and S. Dolfi, Semi-rational solvable groups, J. Group Theory 13 (2010), no. 4, 535-548.   DOI
7 M. R. Darafsheh, Character theory of finite groups: problems and conjectures, In The first IPM-Isfahan workshop on Group Theory, 2015.
8 R. Dark and C. M. Scoppola, On Camina groups of prime power order, J. Algebra 181 (1996), no. 3, 787-802.   DOI
9 L. Dornhoff, Group Representation Theory. Part A, Marcel Dekker, Inc., New York, 1971.
10 The GAP group, GAP-Groups, Algorithms, and Programming, Version 4.7.4, http://www.gap-system.org, 2014.
11 M. Herzog and J. Schonheim, On groups of odd order with exactly two non-central conjugacy classes of each size, Arch. Math. (Basel) 86 (2006), no. 1, 7-10.   DOI
12 G. Higman, Finite groups in which every element has prime power order, J. London Math. Soc. 32 (1957), 335-342.   DOI
13 I. M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976.
14 A. Kh. Zhurtov, Regular automorphisms of order 3 and Frobenius pairs, Siberian Math. J. 41 (2000), no. 2, 268-275; translated from Sibirsk. Mat. Zh. 41 (2000), no. 2, 329-338, ii.   DOI
15 R. Knorr, W. Lempken, and B. Thielcke, The $S_3$-conjecture for solvable groups, Israel J. Math. 91 (1995), no. 1-3, 61-76.   DOI
16 M. L. Lewis, The vanishing-off subgroup, J. Algebra 321 (2009), no. 4, 1313-1325.   DOI
17 J. P. Zhang, Finite groups with many conjugate elements, J. Algebra 170 (1994), no. 2, 608-624.   DOI