Hyperbolic groups of Fibonacci type and T(5) cyclically presented groups

Chinyere, Ihechukwu; Williams, Gerald

doi:10.1016/j.jalgebra.2021.04.003

Cited by 8 publications

(2 citation statements)

References 33 publications

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“…The Tits alternative has been considered for various classes of cyclically presented groups [17,7,22,4,11,28]. In this section we investigate the Tits alternative for the class of groups defined by redundant cyclic presentations.…”

Section: The Tits Alternativementioning

confidence: 99%

Redundant relators in cyclic presentations of groups

Chinyere¹,

Williams²

2021

Preprint

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A cyclic presentation of a group is a presentation with an equal number of generators and relators that admits a particular cyclic symmetry. We characterise the orientable, non-orientable, and redundant cyclic presentations and obtain concise refinements of these presentations. We show that the Tits alternative holds for the class of groups defined by redundant cyclic presentations and that if the number of generators of the cyclic presentation is greater than two then the corresponding group is large. Generalizing and extending earlier results of the authors we describe the star graphs of orientable and non-orientable cyclic presentations and classify the cyclic presentations whose star graph components are pairwise isomorphic incidence graphs of generalized polygons, thus classifying the so-called (m, k, ν)-special cyclic presentations.

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Section: The Tits Alternativementioning

confidence: 99%

Redundant relators in cyclic presentations of groups

Chinyere¹,

Williams²

2021

Preprint

Self Cite

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“…Cyclically presented groups have been an object of various investigations not just from the algebraic point of view as in [1,3,10,13,14,19,39] for example, but also from topological perspectives due to their close connections with the topology of closed orientable 3-manifolds (see for example, [7,8,9,12,26,35,37]). This article takes the former viewpoint and concerns the family of cyclically presented groups of type F from [1], which are defined by presentations…”

Section: Introductionmentioning

confidence: 99%