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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Groups with no free subsemigroups
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by P. Longobardi, M. Maj and A. H. Rhemtulla PDF
Trans. Amer. Math. Soc. 347 (1995), 1419-1427 Request permission


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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 1419-1427
  • MSC: Primary 20F16; Secondary 20F60
  • DOI:
  • MathSciNet review: 1277124