Symmetric subgroups in modular group algebras
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Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical involution of the group algebra KG. We study properties of symmetric subgroups and construct a counterexample to the conjecture by V.Bovdi, which states that V(KG)=<G,S*>, where S* is a set of symmetric units of V(KG).
Konovalov , A & Krivokhata , A G 2008 , ' Symmetric subgroups in modular group algebras ' , Nauk. Visn. Uzhgorod. Univ., Ser. Mat., vol. 9 .
Nauk. Visn. Uzhgorod. Univ., Ser. Mat.,
DescriptionThis preprint is translated from the original journal publication in Russian: A. Konovalov and A. Tsapok, Symmetric subgroups of the normalised unit group of the modular group algebra of a finite p-group, Nauk. Visn. Uzhgorod. Univ., Ser. Mat., 9 (2004), 20–24.
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