Vol. 55, No. 2, 1974

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A density theorem on the number of conjugacy classes in finite groups

Edward Arthur Bertram

Vol. 55 (1974), No. 2, 329–333
Abstract

For each finite group G with k(G) conjugacy classes and order g, it is well known that g < 22k . On the other hand, all groups with a given small k(8) have been determined, and these studies, along with the result that if G is nilpotent then g < 2k, strongly suggest that the bound can be significantly improved. We prove that for each c2 < log 2, almost all integers g n, as n →∞, have the property that for each G of order g, k(G) > (log n)c2.

Mathematical Subject Classification 2000
Primary: 10H25
Secondary: 20D99
Milestones
Received: 22 May 1974
Revised: 26 November 1974
Published: 1 December 1974
Authors
Edward Arthur Bertram