NILPOTENCY OF NORMAL SUBGROUPS HAVING TWO G-CLASS SIZES

作者：Alemany Elena^*; Beltran Antonio; Jose Felipe Maria

来源：Proceedings of the American Mathematical Society, 2011, 139(8): 2663-2669.

DOI：10.1090/S0002-9939-2010-10702-5

Let G be a finite group. If N is a normal subgroup which has exactly two G-conjugacy class sizes, then N is nilpotent. In particular, we show that N is abelian or is the product of a p-group P by a central subgroup of G. Furthermore, when P is not abelian, P/(Z(G) boolean AND P) has exponent p.

• 出版日期2011-8