Isomorphic modular group algebras of semi-complete primary abelian groups
Bull. Korean Math. Soc. 2005 Vol. 42, No. 1, 53-56
Published online March 1, 2005
Peter V. Danchev
Abstract : Suppose $G$ is a semi-complete abelian $p$-group and $FG\cong FH$ as commutative unitary $F$-algebras of characteristic $p$ for any fixed group $H$. Then, it is shown that, $G\cong H$. This improves a result of the author proved in the Proceedings of the American Math. Society (2002) and also completely solves by an another method a long-standing problem of W. May posed in the same Proceedings (1979).
Keywords : semi-complete $p$-groups, direct factors, isomorphisms
MSC numbers : Primary 20C07; Secondary 16U60, 16S34, 20K10, 20K15
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