ISOMORPHISM OF MODULAR GROUP ALGEBRAS OF ABELIAN GROUPS WITH SEMI-COMPLETE p-PRIMARY COMPONENTS
نویسندگان
چکیده
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. Math., 2002), (Proc. Amer. Math. Soc., 2002) and (Bull. Korean Math. Soc., 2005) as well as completely settles a problem posed by W. May in (Proc. Amer. Math. Soc., 1979).
منابع مشابه
A 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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