Rocky Mountain Journal of Mathematics

Semigroup compactifications of Zappa products

H.D. Junghenn and P. Milnes

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Rocky Mountain J. Math., Volume 44, Number 6 (2014), 1903-1921.

First available in Project Euclid: 2 February 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Junghenn, H.D.; Milnes, P. Semigroup compactifications of Zappa products. Rocky Mountain J. Math. 44 (2014), no. 6, 1903--1921. doi:10.1216/RMJ-2014-44-6-1903.

Export citation


  • J. Berglund, H. Junghenn and P. Milnes, Analysis on semigroups: Function spaces, compactifications, representations, John Wiley and Sons, New York, 1989.
  • K. de Leeuw and I. Glicksberg, Applications of almost periodic compactifications, Acta Math. 105 (1961), 63–97.
  • ––––, Almost periodic functions on semigroups, Acta Math. 105 (1961), 99–140.
  • H. Junghenn, Distal compactifications of semigroups, Trans. Amer. Math. Soc. 274 (1982), 379–397.
  • H. Junghenn and B. Lerner, Semigroup compactifications of semidirect products, Trans. Amer. Math. Soc. 265 (1981), 393–404.
  • M. Kunze, Lineare Parallelrechner, Interner Bericht, Tech. Hochschule, Darmstadt, 1982.
  • M. Landstad, On the Bohr compactification of a transformation group, Math. Z. 127 (1972), 167–178.
  • G. Mackey, Products of subgroups and projective multipliers, Coll. Math. Soc. Janos Bolyai 5 (1970), Hilbert Space Operators, Tihany, Hungary.
  • J. Szep, On the structure of groups which can be represented as the product of two subgroups, Acta Sci. Math. Szeged 12 (1950), 57–61.
  • G. Zappa, Sulla costruzione dei gruppi prodotto di due dati sottogruppi permutabili traloro, At. Sec. Cong. Mat. Ital., Bologna, 1942.