Groups with no Free Subsemigroups
Groups with no Free Subsemigroups
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 …