Groups with no free subsemigroups

Author:

Longobardi P.,Maj M.,Rhemtulla A. H.

Abstract

We look at groups which have no (nonabelian) free subsemigroups. It is known that a finitely generated solvable group with no free subsemigroup is nilpotent-by-finite. Conversely nilpotent-by-finite groups have no free subsemigroups. Torsion-free residually finite- p p groups with no free subsemigroups can have very complicated structure, but with some extra condition on the subsemigroups of such a group one obtains satisfactory results. These results are applied to ordered groups, right-ordered groups, and locally indicable groups.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference17 articles.

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2. R. Botto Mura and A.H. Rhemtulla, Orderable groups, Dekker, 1977.

3. P.F. Conrad, Right ordered groups, Michigan Math. J. 6 (1959), 267-275.

4. L. Fuchs, Partially ordered algebraic systems, Pergamon Press, 1963.

5. R. I. Grigorchuk, On the growth degrees of -groups and torsion-free groups, Math. Sb. 126 (1985), 194-214

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