On semi-groups in which xr = x

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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.

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  • On semi-groups
    Mathematical Proceedings of the Cambridge Philosophical Society, 1940