Intersections of Magnus subgroups and embedding theorems for cyclically presented groups

Martin Edjvet; James Howie

doi:10.1016/j.jpaa.2007.04.009

Intersections of Magnus subgroups and embedding theorems for cyclically presented groups

Martin Edjvet, James Howie

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

It is now known that the intersection of two Magnus subgroups M_i = <Y_i > (1 = i = 2) in a one-relator group is either the free group F on Y₁ n Y₂ or the free product of F together with an infinite cyclic group (so-called exceptional intersection). Using this, we give conditions under which two embedding theorems for cyclically presented groups can be obtained. This provides a new method for proving such groups infinite. We also give a combinatorial method for checking the presence of exceptional intersections. © 2007 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	47-52
Number of pages	6
Journal	Journal of Pure and Applied Algebra
Volume	212
Issue number	1
DOIs	https://doi.org/10.1016/j.jpaa.2007.04.009
Publication status	Published - Jan 2008

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10.1016/j.jpaa.2007.04.009

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AB - It is now known that the intersection of two Magnus subgroups Mi = <Yi > (1 = i = 2) in a one-relator group is either the free group F on Y1 n Y2 or the free product of F together with an infinite cyclic group (so-called exceptional intersection). Using this, we give conditions under which two embedding theorems for cyclically presented groups can be obtained. This provides a new method for proving such groups infinite. We also give a combinatorial method for checking the presence of exceptional intersections. © 2007 Elsevier Ltd. All rights reserved.

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Intersections of Magnus subgroups and embedding theorems for cyclically presented groups

Abstract

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