The isomorphism question for modular group algebras of metacyclic $p$-groups
نویسندگان
چکیده
منابع مشابه
ISOMORPHISM OF MODULAR GROUP ALGEBRAS OF ABELIAN GROUPS WITH SEMI-COMPLETE p-PRIMARY COMPONENTS
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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We give a new conceptual proof of the following classical fact due to Karpilovsky (Contemp. Math., 1982) but over finite fields: Let G be a p-mixed abelian group with divisible p-component. If F is a finite field of char(F ) = p, then FH ∼= FG as F -algebras for another group H forces that H ∼= G. Subject Classification: Primary 20C07, 16S34, 16U60; Secondary 20K10, 20K21, 20K25.
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Let L be a restricted Lie algebra with the restricted enveloping algebra u(L) over a perfect field of positive characteristic p. The restricted isomorphism problem asks what invariants of L are determined by u(L). This problem is the analogue of the modular isomorphism problem for finite p-groups. Bagiński and Sandling have given a positive answer to the modular isomorphism problem for metacycl...
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Suppose G is a p-mixed splitting abelian group and R is a commutative unitary ring of zero characteristic such that the prime number p satisfies p / ∈ inv(R)∪ zd(R). Then R(H) and R(G) are canonically isomorphic R-group algebras for any group H precisely when H and G are isomorphic groups. This statement strengthens results due to W.May published in J.Algebra (1976) and to W.Ullery published in...
متن کاملCommutative modular group algebras of p-mixed and p-splitting abelian Σ-groups
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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1988
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1988-0958039-8