CONJUGACY CLASSES IN FINITE GROUPS-II

In this paper we analyze the number of conjugacy classes in a finite group, in terms of the arithmetic structure of its order and, for some refinements of the results, its Sylow structure. The method is elementary, and in particular does not use character theory. Our results improve one of those of Gideon Amit and David Chillag, Houston J. Math. 12 (1986), 1-9, for finite groups of odd order, and a result of Avinoa Mann, Israel J. Math. 31 (1978), 78-84, for groups of even order with abelian Sylow 2-subgroups. Two examples at the end show that our results are in some cases best possible.