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 Isomorphism of modular group algebras of abelian groups with semi-complete $p$-primary components Commun. Korean Math. Soc. 2007 Vol. 22, No. 2, 157-161 Printed June 1, 2007 Peter Danchev 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 MSC numbers : 20C07, 16S34, 16U60, 20K10, 20K15, 20K20, 20K21 Downloads: Full-text PDF

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