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Power-free groups

Published online by Cambridge University Press:  24 October 2008

A. Geddes
A. Geddes
Affiliation:
University of Glasgow
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Extract

1. Introduction. Consider a set P with elements a, b, c,… and a certain distinguished element e. Assume that P satisfies the following conditions.

(I) With each ordered pair (a, b) of distinct elements a and b of P there is associated a unique element of P (to be denoted by ab and called the product of a and b). Further, with the pair (e, e) there is associated a unique element ee of P.

(II)(ab)c = a(bc) for all elements a, b, c in P for which both sides are defined.

(III) ea = a = ae for all elements a ∈ P.

(IV) To each element a ∈ P, there corresponds an element a′ ∈ P such that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 3 , July 1964 , pp. 393 - 408
Copyright
Copyright © Cambridge Philosophical Society 1964

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