New reductions and logarithmic lower bounds for the number of conjugacy classes in finite groups

Authors

  • Edward A. Bertram University of Hawaii at Manoa

Keywords:

group theory

Abstract

The unsolved problem of whether there exists a positive constant c such that the number k(G) of conjugacy classes in any finite group G satisfies k(G) >= c log_2/G/ has attracted attention for many years. Deriving bounds on k(G) from (i.e. reducing the problem to) assumptions about a normal subgroup N (or k(N)) and k(G/N) plays a critical role. Here we obtain new reductions and use these to obtain new logarithmic lower bounds. In some cases we find that for /G/ large (depending on t >= 1), k(G) >= (log /G/)^t . 0.1017/S0004972712000536

Author Biography

Edward A. Bertram, University of Hawaii at Manoa

Mathematics Department,Professor

Published

2013-04-29

Issue

Vol. 87 No. 3 (2013)

Section

Articles
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