A problem in the Kourovka notebook concerning the number of conjugacy classes of a finite group

Details A problem in the Kourovka notebook concerning the number of conjugacy classes of a finite group A problem in the Kourovka notebook concerning the number of conjugacy classes of a finite group

2008-10-30

arxiv.org/abs/0810.5494v1

Mathematics

Group Theory

25 pages

Scientific paper

In this paper, we consider Problem 14.44 in the Kourovka notebook, which is a conjecture about the number of conjugacy classes of a finite group. While elementary, this conjecture is still open and appears to elude any straightforward proof, even in the soluble case. However, we do prove that a minimal soluble counterexample must have certain properties, in particular that it must have Fitting height at least 3 and order at least 2000.

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