Vol. 73, No. 1, 1977

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Semidirect product of semigroups in relation to amenability, cancellation properties, and strong Følner conditions

Maria M. Klawe

Vol. 73 (1977), No. 1, 91–106

The purpose of this paper is to settle two problems. The first is Sorenson’s conjecture on whether every right cancellative left amenable semigroup is lefl cancellative. The second, posed by Argabright and Wilde, is whether every left amenable semigroup satisfies the strong Følner condition (SFC). We first show that these two problems are equivalent, then prove that the answer to both questions is no, through analyzing the semidirect product of semigroups in relation to amenability and cancellation properties. We conclude by investigating further the properties of semigroups satisfying SFC, and finally include some analogous results for left measurable semigroups.

Mathematical Subject Classification 2000
Primary: 43A07
Received: 3 January 1977
Revised: 11 April 1977
Published: 1 November 1977
Maria M. Klawe