Semigroups with a dense subgroup

Author:
W. S. Owen

Journal:
Trans. Amer. Math. Soc. **212** (1975), 219-228

MSC:
Primary 22A15

MathSciNet review:
0412330

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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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1975-0412330-8

Keywords:
Completely semisimple semigroup,
dense Lie subgroup,
Green's relations,
local cross section,
locally compact orbit

Article copyright:
© Copyright 1975
American Mathematical Society