On the Freiheitssatz in Certain One-Relator Free Products. Iii

Shwartz, Robert

doi:10.1017/s0013091599001224

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…Therefore to study the equation r(t) = 1 it is sufficient to study the group G and this has been our approach. We end this section by mentioning that types I and II have been studied by Schwartz [9].…”

Section: Equations Over Groupsmentioning

confidence: 99%

“…Here we shall give a more, but not fully, complete account of this last case. (m, n) ∈ { (2,2), (2,6), (3,9), (4,4), (4,12), (5,5), (5,15), (6,18)} .…”

Section: Introductionmentioning

confidence: 99%

“…Our first result yields Theorem A(i), Theorem B(i) and Theorem B(ii).Proposition 7. (i) If 2 m 6 then (m, n) ∈ NC if and only if (m, n) ∈ {(2,2),(2,6),(3,9),(4,4),(4, 12),(5,5),(5, 15),(6, 18)}. (ii) If 2 n 6 then (m, n) ∈ NC if and only if (m, n) ∈ {(2,2),(7,3),(4,4),(5,5),(2,6),(7,6), (14, 6)}.…”

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confidence: 99%

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Equations of length 4 and one-relator products

Edjvet

Juhász

2000

Math. Proc. Camb. Phil. Soc.

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This paper continues our study started in [5] of the group G defined by the presentationformula herewhere m [ges ] 2, n [ges ] 2 and ∈i = ±1 for 1 [les ] i [les ] 2. The problem under consideration can be stated as: precisely when does both a have order m and b have order n in the group G? This question arose as a result of our investigation into equations over groups and the connection is explained in Section 2.

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Section: Equations Over Groupsmentioning

confidence: 99%

“…Here we shall give a more, but not fully, complete account of this last case. (m, n) ∈ { (2,2), (2,6), (3,9), (4,4), (4,12), (5,5), (5,15), (6,18)} .…”

Section: Introductionmentioning

confidence: 99%

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Equations of length 4 and one-relator products

Edjvet

Juhász

2000

Math. Proc. Camb. Phil. Soc.

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One-Relator Products Induced from Generalized Triangle Groups

Howie

Shwartz

2004

Communications in Algebra

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Abstract. We study the quotient of a free product of groups by the normal closure of a word that is contained in a certain type of 2-generator subgroup, and hence can be expressed in the form of a pushout involving a generalized triangle group. Using the theory of generalized triangle groups, we extend the range of conditions under which a number of results for one-relator products of groups, such as the Freiheitssatz and the solubility of the word problem, are known to hold.

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Largeness and Sq-Universality of Cyclically Presented Groups

Williams

2012

Int. J. Algebra Comput.

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Largeness, SQ-universality, and the existence of free subgroups of rank 2 are measures of the complexity of a finitely presented group. We obtain conditions under which a cyclically presented group possesses one or more of these properties. We apply our results to a class of groups introduced by Prishchepov which contain, amongst others, the various generalizations of Fibonacci groups introduced by Campbell and Robertson. Using the techniques developed we give a new, purely group-theoretic, proof of the (almost complete) classification of the finite Cavicchioli-HegenbarthRepovš groups.

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On the Freiheitssatz in Certain One-Relator Free Products. Iii

Abstract: We study one-relator free products in which the relator has free-product length 4. We find conditions for such presentations to have a Freiheitssatz and classify all non-aspherical presentations under certain conditions.

Cited by 3 publications

References 11 publications

Equations of length 4 and one-relator products

Equations of length 4 and one-relator products

One-Relator Products Induced from Generalized Triangle Groups

Largeness and Sq-Universality of Cyclically Presented Groups

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