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.