GROUPS WITH COMMUTING POWERS

Author:

BRANDL ROLF

Abstract

AbstractA group G satisfies the second Engel condition [X,Y,Y ]=1 if and only if x commutes with xy, for all x,yG. This paper considers the generalization of this condition to groups G such that, for fixed positive integers r and s, xr commutes with (xs)y for all x,yG. Various general bounds are proved for the structure of groups in the corresponding variety, defined by the law [Xr,(Xs)Y]=1.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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