This article is cited in 1 paper

Finite nilpotent groups with relatively large centralizers of noninvariant subgroups

V. A. Antonov, T. G. Nozhkina

Chair of General Mathematics, Southern Ural State University, Chelyabinsk, Russia

Abstract: We study groups where every noninvariant subgroup satisfies the following condition: the index of the product of this subgroup and its centralizer in the normalizer of this subgroup divides prime number fixed for the given group. We fully describe two-step nilpotent $p$-groups with the mentioned property.

Keywords: group, noninvariant subgroup, centralizer, normalizer, index.

UDC: 512.54

Received: 17.08.2010

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:10, 9–12

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