Bounds on the number of conjugacy classes of the symmetric and\n alternating groups

2016/07/21 by Bret J. Benesh, Benesh, Bret, Cong T. S. Van +1
Mathematics · Engineering · #Finite Group Theory Research #graph theory and CDMA systems #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1607.06456

Abstract

Let G be a finite group with Sylow subgroups P₁,\…,P_n, and let\nk(G) denote the number of conjugacy classes of G. Pyber asked if k(G) \≤\n\∏_i=1ⁿ k(P_i) for all finite groups G. With the help of GAP, we prove\nthat Pyber's inequality holds for all symmetric and alternating groups.\n

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