A new simple proof of the W. May’s claim: \(FG\) determines \(G/G_0\). (English) Zbl 1019.20002

Let \(G\) be an Abelian group with torsion part \(G_0\) and let \(F\) be a field of arbitrary characteristic. A well known result of W. May asserts that if \(FG\) and \(FH\) are isomorphic \(F\)-algebras for any group \(H\), then \(G/G_0\cong H/H_0\). In the present paper the author gives another proof of this fact only in group terms.


20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
16S34 Group rings
16U60 Units, groups of units (associative rings and algebras)
20K21 Mixed groups