Idempotents in complex group rings: Theorems of Zalesskij and Bass revisited.
Improving tameness for metabelian groups.
Infinite dimensional linear groups with many G - invariant subspaces
Let F be a field, A be a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dim F(B/Core G(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char F.
Isomorphism of commutative group algebras of -mixed splitting groups over rings of characteristic zero
Suppose is a -mixed splitting abelian group and is a commutative unitary ring of zero characteristic such that the prime number satisfies . Then and are canonically isomorphic -group algebras for any group precisely when and are isomorphic groups. This statement strengthens results due to W. May published in J. Algebra (1976) and to W. Ullery published in Commun. Algebra (1986), Rocky Mt. J. Math. (1992) and Comment. Math. Univ. Carol. (1995).
Isomorphism of Commutative Modular Group Algebras
∗ The work was supported by the National Fund “Scientific researches” and by the Ministry of Education and Science in Bulgaria under contract MM 70/91.Let K be a field of characteristic p > 0 and let G be a direct sum of cyclic groups, such that its torsion part is a p-group. If there exists a K-isomorphism KH ∼= KG for some group H, then it is shown that H ∼= G. Let G be a direct sum of cyclic groups, a divisible group or a simply presented torsion abelian group. Then KH ∼= KG as K-algebras...
Isomorphism of modular group algebras of direct sums of torsion-complete abelian -groups
Isomorphism of noncommutative group algebras of torsion-free groups over a field.