Displaying similar documents to “Isomorphism of commutative group algebras of $p$-mixed splitting groups over rings of characteristic zero”

Commutative modular group algebras of p -mixed and p -splitting abelian Σ -groups

Peter Vassilev Danchev (2002)

Commentationes Mathematicae Universitatis Carolinae

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Let G be a p -mixed abelian group and R is a commutative perfect integral domain of char R = p > 0 . Then, the first main result is that the group of all normalized invertible elements V ( R G ) is a Σ -group if and only if G is a Σ -group. In particular, the second central result is that if G is a Σ -group, the R -algebras isomorphism R A ≅ R G between the group algebras R A and R G for an arbitrary but fixed group A implies A is a p -mixed abelian Σ -group and even more that the high subgroups of A and G are isomorphic, namely,...

A note on group algebras of p -primary abelian groups

William Ullery (1995)

Commentationes Mathematicae Universitatis Carolinae

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Suppose p is a prime number and R is a commutative ring with unity of characteristic 0 in which p is not a unit. Assume that G and H are p -primary abelian groups such that the respective group algebras R G and R H are R -isomorphic. Under certain restrictions on the ideal structure of R , it is shown that G and H are isomorphic.

On commutative twisted group rings

Todor Zh. Mollov, Nako A. Nachev (2005)

Czechoslovak Mathematical Journal

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Let G be an abelian group, R a commutative ring of prime characteristic p with identity and R t G a commutative twisted group ring of G over R . Suppose p is a fixed prime, G p and S ( R t G ) are the p -components of G and of the unit group U ( R t G ) of R t G , respectively. Let R * be the multiplicative group of R and let f α ( S ) be the α -th Ulm-Kaplansky invariant of S ( R t G ) where α is any ordinal. In the paper the invariants f n ( S ) , n ∈ ℕ ∪ { 0 } , are calculated, provided G p = 1 . Further, a commutative ring R with identity of prime characteristic...