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On semi-groups in which xr = x

Published online by Cambridge University Press:  24 October 2008

J. A. Green  and
D. Rees
J. A. Green
Affiliation:
Victoria UniversityManchester
D. Rees
Affiliation:
Downing CollegeCambridge
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Extract

In this note we are concerned with the semi-group Snr, generated by n of its elements, in which each element x satisfies the equation xr = x, the semi-group being otherwise free. The main result proved is that the proposition

(Ar) Snris finite for all finite n, is equivalent to the proposition

(Br) the group Bn, r−1, generated by n of its elements, in which each element x satisfies the equation xr−1 = 1, the group being otherwise free, is finite for all finite n.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 1 , January 1952 , pp. 35 - 40
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

REFERENCE

(1)Rees, D.On semigroups. Proc. Camb. phil. Soc. 36 (1939), 387–400.Google Scholar