[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2007.22.2.157

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

Publication Information

Communications of the Korean Mathematical Society / v.22, no.2, 2007 , pp. 157-161 More about this Journal

Abstract

Let G be a p-mixed abelian group with semi-complete torsion subgroup $G_t$ 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;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)
Times Cited By SCOPUS : 0

Reference
Cited By KSCI

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