ISOMORPHISM OF MODULAR GROUP ALGEBRAS OF ABELIAN GROUPS WITH SEMI-COMPLETE p-PRIMARY COMPONENTS

Title & Authors
ISOMORPHISM OF MODULAR GROUP ALGEBRAS OF ABELIAN GROUPS WITH SEMI-COMPLETE p-PRIMARY COMPONENTS
Danchev, Peter;

Abstract
Let G be a p-mixed abelian group with semi-complete torsion subgroup $\small{G_t}$ 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).
Keywords
group algebras;isomorphisms;semi-complete groups;p-mixed splitting groups;p-mixed groups with torsion-free rank one;
Language
English
Cited by
1.
MODULAR ABELIAN GROUP ALGEBRAS, Asian-European Journal of Mathematics, 2010, 03, 02, 275
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