Wreath products in modular group algebras of some finite 2-groups

Details Wreath products in modular group algebras of some finite 2-groups Wreath products in modular group algebras of some finite 2-groups

2007-04-25

arxiv.org/abs/0704.3355v1

Acta Mathematica Academiae Paedagogiace Nyiregyhaziensis, Vol.23, No.2, 2007, p.125-127

Mathematics

Rings and Algebras

3 pages

Scientific paper

Let $K$ be field of characteristic 2 and let $G$ be a finite non-abelian 2-group with the cyclic derived subgroup $G'$, and there exists a central element $z$ of order 2 in $Z(G) \backslash G'$. We prove that the unit group of the group algebra $KG$ possesses a section isomorphic to the wreath product of a group of order 2 with the derived subgroup of the group $G$, giving for such groups a positive answer to the question of A. Shalev.

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