Open Access
2014 Semigroup compactifications of Zappa products
H.D. Junghenn, P. Milnes
Rocky Mountain J. Math. 44(6): 1903-1921 (2014). DOI: 10.1216/RMJ-2014-44-6-1903


A group $G$ with subgroups $S$ and $T$ satisfying $G = ST$ and $S\cap T = \{e\}$ gives rise to functions $[t,s] \in S$ and $\\lt t,s\> \in T$ such that $(st)(s't') = (s[t,s'])(\\lt t,s'\>t')$. This notion may be extended to arbitrary semigroups $S$, $T$ with identities, producing the Zappa product of $S$ and $T$, a generalization of direct and semidirect product. Necessary and sufficient conditions are given for a semigroup compactification of a Zappa product $G$ of topological semigroups $S$ and $T$ to be canonically isomorphic to a Zappa product of compactifications of $S$ and $T$. The result is applied to various types of compactifications of $G$, including the weakly almost periodic and almost periodic compactifications.


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H.D. Junghenn. P. Milnes. "Semigroup compactifications of Zappa products." Rocky Mountain J. Math. 44 (6) 1903 - 1921, 2014.


Published: 2014
First available in Project Euclid: 2 February 2015

zbMATH: 1311.22003
MathSciNet: MR3310954
Digital Object Identifier: 10.1216/RMJ-2014-44-6-1903

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.44 • No. 6 • 2014
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