On Tamura’s identity yx=f(x,y) in groups
Primož Moravec · Communications in Algebra · 2019
The purpose of this article is to study the groups satisfying the law yx=xa1yb1xa2yb2, where ai and bi are positive integers. Tamura posed a problem as to when such a law implies that a group is abelian. We show that, apart from obvious reasons why such a variety should contain non-abelian groups, every elementary amenable or residually finite group satisfying such a law has to be abelian.