Semigroups with a dense subgroup

Owen, W. S.

doi:10.1090/S0002-9947-1975-0412330-8

Semigroups with a dense subgroup
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by W. S. Owen PDF

Trans. Amer. Math. Soc. 212 (1975), 219-228 Request permission

Abstract:

The purpose of this paper is twofold. First, it is shown that the ideal structure of a semigroup with dense subgroup is closely related to its transformation group structure. That is, if a left orbit through a given point is locally compact, then the members of this orbit are precisely those elements which generate the same left ideal as the given point. Secondly, the author gives a number of theorems which have as their goal the establishment of a natural product structure near a nonzero idempotent. Specifically the work of F. Knowles [11] is improved upon to include (1) the possibility of a nonconnected group; (2) the possibility of a nonsimply connected orbit; and (3) the case in which the boundary of the group is more than a single orbit.

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