The notion of semidirect product of two transformation semigroups is introduced, and its space of almost periodic functions is expressed as a tensor product. The general techniques developed are applied to the special case of a semidirect product S © T of two semigroups. As a consequence new results are obtained on the characterization of the almost periodic compactification of S © Γ as a semidirect product of compact semigroups. A related result is the splitting of the enveloping semigroup of

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... semidirect product of certain flows into a semidirect product of enveloping semigroups. Introduction. Let S and T be semitopological semigroups