Groups with no free subsemigroups

Authors:
P. Longobardi, M. Maj and A. H. Rhemtulla

Journal:
Trans. Amer. Math. Soc. **347** (1995), 1419-1427

MSC:
Primary 20F16; Secondary 20F60

DOI:
https://doi.org/10.1090/S0002-9947-1995-1277124-5

MathSciNet review:
1277124

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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- 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.

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DOI:
https://doi.org/10.1090/S0002-9947-1995-1277124-5

Article copyright:
© Copyright 1995
American Mathematical Society