Isomorphism of commutative group algebras of $p$-mixed splitting groups over rings of characteristic zero

Peter Vassilev Danchev

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.

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

A note on group algebras of p -primary abelian groups

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

A note on group algebras of $p$ -primary abelian groups