Vol. 36, No. 1, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
The index of a group in a semigroup

George M. Bergman

Vol. 36 (1971), No. 1, 55–62

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
Received: 21 April 1970
Published: 1 January 1971
George M. Bergman
Department of Mathematics
University of California Berkeley
Berkeley CA 94720-3840
United States