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A unitary subgroup of the multiplicative group of a modular group algebra of a finite Abelian p-group. (Russian) Zbl 0674.16007
Let U(KG) be the multiplicative group of the group algebra KG of the abelian p-group G over a field K with char K\(=p\) and let V(KG) be the normed multiplicative subgroup of U(KG). If \(x=\sum_{g\in G}\alpha_ gg\in KG\) let \(x^*=\sum_{g\in G}\alpha_ gg^{-1}\). Then \(V_*(KG)=\{u\in V(KG)|\) \(u^{-1}=u^*\}\) is a subgroup of V(KG). In this paper the authors describe the structure of \(V_*(KG)\) when G is a finite abelian p-group and K is a finite field. Furthermore, they indicate a basis for \(V_*(KG)\) when \(p>2\).
Reviewer: S.V.Mihovski

16U60 Units, groups of units (associative rings and algebras)
16S34 Group rings
20C05 Group rings of finite groups and their modules (group-theoretic aspects)