This article is cited in 6 papers

Finite Alperin 2-groups with cyclic second commutants

B. M. Veretennikov

Ural State Technical University, Ekaterinburg, Russia

Abstract: An Alperin group is a group in which every 2-generated subgroup has a cyclic commutant. Previously, we constructed examples of finite Alperin 2-groups with second commutant isomorphic to $Z_2$ or $Z_4$. Here, it is proved that for any natural $n$, there exists a finite Alperin 2-group whose second commutant is isomorphic to $Z_{2^n}$.

Keywords: 2-group, Alperin group, commutant, representation of groups in terms of generators and defining relations.

UDC: 512.54

Received: 24.03.2010

 English version: Algebra and Logic, 2011, 50:3, 226–244

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