Vol. 36, No. 1, 1971

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ISSN: 0030-8730
The index of a group in a semigroup

George M. Bergman

Vol. 36 (1971), No. 1, 55–62
Abstract

We shall define the right and left indices of a subgroup G in a semigroup S with unit, and show that if G has cancellation in S, and at least one of these indices is finite, then they are equal. If only right cancellation holds, and the left index is finite, the right index will be either less than the left index, or infinite. It will be shown by counterexamples that these theorems are “best results.”

Mathematical Subject Classification
Primary: 20.93
Milestones
Received: 21 April 1970
Published: 1 January 1971
Authors
George M. Bergman
Department of Mathematics
University of California Berkeley
Berkeley CA 94720-3840
United States
http://math.berkeley.edu/~gbergman/