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Some group laws equivalent to the commutative law

Published online by Cambridge University Press:  17 April 2009

J. M. Gandhi
J. M. Gandhi
Affiliation:
York University, Toronto, Canada, and Western lllinois University, Macomb, lllinois, USA.
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Abstract

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In this paper we prove the Theorem: A group satisfying the law (1) [x, y] = [u, v, w], where u, v, w are the entries from the set {x, x-1, y, y-1} is always abelian. Earlier a few cases of this theorem were proved by Gupta. It is also proved that a group satisfying the law = [x, y, x] is always abelian.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 2 , Issue 3 , June 1970 , pp. 335 - 345
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Gupta, N.D., “Some group-laws equivalent to the commutative law”, Arch. Math. 17 (1966), 97–102.CrossRefGoogle Scholar
[2]Hall, Marshall Jr, The theory of groups (Macmillan, New York, 1959).Google Scholar