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Non-cancellative power-free groups

Published online by Cambridge University Press:  18 May 2009

R. G. Walker
R. G. Walker
Affiliation:
University of GlasgowGlasgow, W.2
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A. Geddes [1, Theorem 3.3] has shown that the partial algebraic system which he has called a power-free group need not be cancellative. In other words, there exist power-free groups containing at least one element a with the property that ab can equal ac when b ≠ c. In the present paper we propose to study the structure of such non-cancellative power-free groups, and we shall in fact obtain a complete solution to this problem.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 4 , July 1966 , pp. 207 - 212
Copyright
Copyright © Glasgow Mathematical Journal Trust 1966

References

REFERENCES

1.Geddes, A., Power-free groups, Proc. Cambridge Philos. Soc. 60 (1964), 393–408.CrossRefGoogle Scholar
2.Geddes, A. and Walker, R. G., The structure of cancellative power-free groups, Proc. Glasgow Math. Assoc. 7 (1966), 199–206.CrossRefGoogle Scholar