Modular group algebras of totally projective $p$-primary 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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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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Let F be an algebraically closed field of characteristic p > 0 and G be a quasi-simple group with G/Z(G) ∼= An. We describe the minimal polynomials of elements of order p in irreducible representations of G over F . If p = 2 we determine the minimal polynomials of elements of order 4 in 2modular irreducible representations of An, Sn, 3 ·A6, 3 ·S6, 3 ·A7, and 3 ·S7.
متن کاملA Note on the Isomorphism of Modular Group Algebras of p-Mixed Abelian Groups with Divisible p-Components
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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1979
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1979-0534384-x