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The structure of cancellative power-free groups

Published online by Cambridge University Press:  18 May 2009

A. Geddes  and
R. G. Walker
A. Geddes
Affiliation:
University of GlasgowGlasgow, W.2
R. G. Walker
Affiliation:
University of GlasgowGlasgow, W.2
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The definition of a power-free group will be found in [1]. It is a partial algebraic system which, roughly speaking, may be thought of as a group in which (with the exception of the identity) squares and higher powers of an element are not defined.

It has been shown [1, Theorem 3.3] that the usual cancellation laws need not hold in a power-free group. When these laws do hold, the power-free group is called cancellative. In this paper we shall be solely concerned with cancellative power-free groups and the term ‘power-free group’ is to be understood to mean ‘cancellative power-free group’.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 4 , July 1966 , pp. 199 - 206
Copyright
Copyright © Glasgow Mathematical Journal Trust 1966

References

REFERENCE

1.Geddes, A., Power-free groups, Proc. Cambridge Philos. Soc. 60 (1964), 393–408.CrossRefGoogle Scholar