Amenability and Right Orderable Groups

Kropholler, Peter H.

doi:10.1112/blms/25.4.347

Cited by 5 publications

(2 citation statements)

References 7 publications

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“…Our result thus extends the well-known result that nilpotent-by-finite right orderable groups are locally indicable. It also extends a recent result of Kropholler in [ 10] that the convex subgroups of a right-ordered supramenable group form a series with torsion-free abelian factors. This follows since supramenable groups contain no free semigroups [14, p. 189].…”

Section: Introductionmentioning

confidence: 48%

Groups with no Free Subsemigroups

Longobardi¹,

Maj²,

Rhemtulla³

1995

Transactions of the American Mathematical Society

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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-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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Section: Introductionmentioning

confidence: 48%

Groups with no Free Subsemigroups

Longobardi¹,

Maj²,

Rhemtulla³

1995

Transactions of the American Mathematical Society

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“…Recall that a group is termed indicable if it has a homomorphism onto the infinite cyclic group. Indicable groups play an important role in the study of right orderable groups, amenability and bounded cohomology (See [11,12,15]).…”

Section: Introductionmentioning

confidence: 99%

Indicable Groups and Endomorphic Presentations

Benli

2011

Glasgow Math. J.

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In this paper we look at presentations of subgroups of finitely presented groups with infinite cyclic quotients. We prove that if H is a finitely generated normal subgroup of a finitely presented group G with G/H cyclic, then H has ascending finite endomorphic presentation. It follows that any finitely presented indicable group without free semigroups has the structure of a semidirect product H ⋊ ℤ, where H has finite ascending endomorphic presentation.

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