Geodesic
Products of Locally Compact Groups with Zero and Their Actions
Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1043-1051

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In [4], Hofmann defines a locally compact group with zero as a Hausdorff locally compact topological semigroup, S, with a non-isolated point, 0, such that G = S — {0} is a group. He shows there that 0 is indeed a zero for 5, G is a locally compact topological group, and the identity of G is the identity of S. The author has investigated actions of such semigroups on locally compact spaces in [1; 2]. In this paper, we are investigating direct products of semigroups of the above type and actions of these products; for a special case of this, the reader is referred to [3]. 
Hanson, T. H. McH. Products of Locally Compact Groups with Zero and Their Actions. Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1043-1051. doi: 10.4153/CJM-1972-106-6
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[1] 1. Hanson, T. H. McH., Actions of a locally compact group with zero, Can. J. Math. 23 (1971), 413–420. Google Scholar

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