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GROUPS WITH COMMUTING POWERS

Published online by Cambridge University Press:  13 March 2009

ROLF BRANDL*
Affiliation:
Mathematisches Institut, Am Hubland 12, 97074 Würzburg, Germany
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Abstract

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A 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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2009

References

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