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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Structure of the semigroup of semigroup extensions

Authors: R. O. Fulp and J. W. Stepp
Journal: Trans. Amer. Math. Soc. 158 (1971), 63-73
MSC: Primary 22.05
MathSciNet review: 0277651
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Abstract: Let $B$ denote a compact semigroup with identity and $G$ a compact abelian group. Let $\operatorname {Ext} (B,G)$ denote the semigroup of extensions of $G$ by $B$. We show that $\operatorname {Ext} (B,G)$ is always a union of groups. We show that it is a semilattice whenever $B$ is. In case $B$ is also an abelian inverse semigroup with its subspace of idempotent elements totally disconnected, we obtain a determination of the maximal groups of a commutative version of $\operatorname {Ext} (B,G)$ in terms of the extension functor of discrete abelian groups.

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Keywords: Extension of compact semigroups, groups by semigroups, groups by semilattices, groups by inverse semigroups, character groups, inverse systems of groups
Article copyright: © Copyright 1971 American Mathematical Society