Modular group algebras of simply presented abelian groups
نویسندگان
چکیده
منابع مشابه
ON ALMOST ω1-n-SIMPLY PRESENTED ABELIAN p-GROUPS
We define and investigate the class of almost ω1-n-simply presented p-torsion abelian groups, which class properly contains the subclasses of almost n-simply presented groups and ω1-n-simply presented groups, respectively. The obtained results generalize those obtained by us in Korean J. Math. (2014) and J. Algebra Appl. (2015).
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Let G be a p-mixed abelian group with semi-complete torsion subgroup Gt such that G is splitting or is of torsion-free rank one, and let R be a commutative unitary ring of prime characteristic p. It is proved that the group algebras RG and RH are R-isomorphic for any group H if and only if G and H are isomorphic. This isomorphism relationship extends our earlier results in (Southeast Asian Bull...
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Let G be a p-mixed abelian group and R is a commutative perfect integral domain of charR = p > 0. Then, the first main result is that the group of all normalized invertible elements V (RG) 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 RA ∼= RG between the group algebras RA and RG for an arbitrary but fi...
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In this note we study the commutative modular and semisimple group rings of σ-summable abelian p-groups, which group class was introduced by R. Linton and Ch. Megibben. It is proved that S(RG) is σ-summable if and only if Gp is σ-summable, provided G is an abelian group and R is a commutative ring with 1 of prime characteristic p, having a trivial nilradical. If Gp is a σ-summable p-group and t...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1988
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1988-0962805-2