6 research outputs found
On the isomorphism problem for unit groups of modular group algebras
Using the computational algebra system GAP (http://www.gap-system.org) and
the GAP package LAGUNA (http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm), we
checked that all 2-groups of order not greater than 32 are determined by
normalized unit groups of their modular group algebras over the field of two
elements.Comment: 6 pages, accepted in Acta Sci. Math. (Szeged
Symmetric subgroups in modular group algebras
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)=, where S* is a set of symmetric units of V(KG).Comment: 5 pages, translated from original journal publication in Russia
Symmetric subgroups in modular group algebras
This 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.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)=, where S* is a set of symmetric units of V(KG).PreprintPeer reviewe
Symmetric subgroups in modular group algebras
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)