Some Sufficient conditions for a group to be abelian

Authors : Gary WALLS

Pages : 1776-1780

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Publication Date : 0000-00-00

Article Type : Research Paper

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` are replaced by arbitrary elements of the group then the equation $w=1$ is satisfied. This paper studies certain equations in words, as above, which together with other conditions imply that groups which satisfy these equations and conditions must be abelian.
Keywords : Group laws, commutators, abelian groups