On semi-groups in which xr = x
- 1 January 1952
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 48 (1), 35-40
- https://doi.org/10.1017/s0305004100027341
Abstract
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.Keywords
This publication has 1 reference indexed in Scilit:
- On semi-groupsMathematical Proceedings of the Cambridge Philosophical Society, 1940