Embedding of groups and quadratic equations over groups

Cummins, Desmond F.; Ivanov, Sergey

doi:10.48550/arxiv.1607.06784

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2016

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“…is the reduced rank of a free group F and |T | is the cardinality of a finite set T . Recall that, according to our notation, the number of nonoriented edges of W s is 1 2…”

Section: Preliminariesmentioning

confidence: 99%

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On rank of the join of two subgroups in a free group

Ivanov

2016

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Let H, K be two finitely generated subgroups of a free group, let H, K denote the subgroup generated by H, K, called the join of H, K, and let neither of H, K have finite index in H, K . We prove the existence of an epimorphism ζ : H, K → F 2 , where F 2 is a free group of rank 2, such that the restriction of ζ on both H and K is injective and the restrictionis surjective. This is obtained as a corollary of an analogous result on rank of the generalized join of two finitely generated subgroups in a free group.

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“…is the reduced rank of a free group F and |T | is the cardinality of a finite set T . Recall that, according to our notation, the number of nonoriented edges of W s is 1 2…”

Section: Preliminariesmentioning

confidence: 99%

“…It is a recurring theme in group theory to embed a countable group into a 2generated group often with some additional properties, see [1], [3], [4], [7], [11]. In this article we will look at two finitely generated subgroups of a free group from a similar perspective.…”

Section: Introductionmentioning

confidence: 99%

On rank of the join of two subgroups in a free group

Ivanov

2016

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Embedding of groups and quadratic equations over groups

Cited by 1 publication

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On rank of the join of two subgroups in a free group

On rank of the join of two subgroups in a free group

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