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- $p$ 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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- © Copyright 1995 American Mathematical Society
- 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