Solution of the Membership Problem for Magnus Subgroups in Certain One-Relator Free Products

Juhász, Arye

doi:10.1007/978-3-7643-8412-8_10

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“…?/, and hence proves Theorem C. We remark that it also implies several results of different nature. In [Ju5] we solved the membership problem for Magnus subgroups of one-relator free products with small cancellation. In [Ju6] we proved the appropriate version of Magnus's Freiheitssatz for Magnus subsemigroups of one-relator groups with small cancellation.…”

Section: Moreover If R Has No Cyclic Conjugate R As Inmentioning

confidence: 99%

“…The next section is devoted to the improved version of Greendlinger's Lemma. A similar version was formulated in [Ju5] the proof of which, using Lemmas 2.3 and 2.11, easily can be adapted to the proof of Proposition 2.12 below. Therefore, we shall omit the details of the proof, which consists of case by case checking.…”

Section: Thenˆá/ Contains No Cyclic Conjugate Of A˙1mentioning

confidence: 99%

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Magnus intersections of one-relator free products with small cancellation conditions

Juhász¹

2007

Groups Geom. Dyn.

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Abstract. Donald Collins initiated the study of intersections of Magnus subgroups in onerelator groups. In particular, he characterized those intersections of Magnus subgroups that are not Magnus subgroups. In the present work we show that Collins' results extend to one-relator quotients of free products of groups with a small cancellation condition and give a complete list of those defining relators for which Magnus subgroups do not intersect in a Magnus subgroup. We use van Kampen diagrams and word combinatorics.

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Section: Moreover If R Has No Cyclic Conjugate R As Inmentioning

confidence: 99%

Section: Thenˆá/ Contains No Cyclic Conjugate Of A˙1mentioning

confidence: 99%