Some Sufficient conditions for a group to be abelian

Abstract

A group is said to satisfy a word w in the symbols ${x,x^{-1},;y,y^{-1}}$ provided that if the ’x’ and ’y’ arereplaced by arbitrary elements of the group then the equation w = 1 is satisfied. This paper studies certain equationsin words, as above, which together with other conditions imply that groups which satisfy these equations and conditionsmust be abelian.