ON A QUESTION OF W. L. MAY CONCERNING THE ISOMORPHISM OF MODULAR GROUP ALGEBRAS

Abstract

In 1988, Warren Lee May has asked in the Proceedings of the American Mathematical Society the following: Let G be an abelian group whose p-component G _p is simply presented andlet F be a field of char F = p > 0. Then whether the F-isomorphism FH ≅ FG for any group H implies that H _p ≅ G _p ? The first actual positive answer isgiven by us in 1997 again in these Proceedings for the particular case when length G _p < Ω. Here we shall establish an elegant positive solution of the question when length G _p < Ω² but only over the field of p-elements F _p , utilizing a new criterion for simply presentedness with length Ω in the terms of summable p-groups.

ACKNOWLEDGMENTS

The author would like to thank to the referee for the help this article to be more explicitly written. Besides, the author is grateful to the Editor Professor Kenneth Goodearl for the care to the present work.