Finitely presented groups of Fibonacci type. part II

Campbell, C. M.; Robertson, E. F.

doi:10.1017/s1446788700015755

Cited by 5 publications

(1 citation statement)

References 5 publications

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“…Thus there is the following almost complete classification of the finite groups H(n, t): Corollary 6.5 Suppose n ≥ 2, t ≥ 0, (n, t) = (9, 4), (9,7). Then H(n, t) is finite if and only if t = 0, 1 or (n, t) = (2k, k + 1) where k ≥ 1 (in which case H(n, t) ∼ = Z 2 k +1 ), or (n, t) = (3, 2), (4, 2), (5, 2), (5, 3), (5,4), (6,3), (7,4), (7,6), (8,3).…”

Section: Theorem 64 ([23])mentioning

confidence: 99%

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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Section: Theorem 64 ([23])mentioning

confidence: 99%

Largeness and Sq-Universality of Cyclically Presented Groups

Williams

2012

Int. J. Algebra Comput.

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Some group theoretic examples with completion theorem provers

Linton

Shand

1996

J Autom Reasoning

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Efficient finite groups arising in the study of relative asphericity

Bogley

Williams

2016

Math. Z.

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We study a class of two-generator two-relator groups, denoted J n (m, k), that arise in the study of relative asphericity as groups satisfying a transitional curvature condition. Particular instances of these groups occur in the literature as finite groups of intriguing orders. Here we find infinite families of non-elementary virtually free groups and of finite metabelian non-nilpotent groups, for which we determine the orders. All Mersenne primes arise as factors of the orders of the non-metacyclic groups in the class, as do all primes from other conjecturally infinite families of primes. We classify the finite groups up to isomorphism and show that our class overlaps and extends a class of groups F a,b,c with trivalent Cayley graphs that was introduced by C.M.Campbell, H.S.M.Coxeter, and E.F.Robertson. The theory of cyclically presented groups informs our methods and we extend part of this theory (namely, on connections with polynomial resultants) to "bicyclically presented groups" that arise naturally in our analysis. As a corollary to our main results we obtain new infinite families of finite metacyclic generalized Fibonacci groups.Part of this research was carried out during a visit by the second named author to the

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Finitely presented groups of Fibonacci type. part II

Cited by 5 publications

References 5 publications

Largeness and Sq-Universality of Cyclically Presented Groups

Largeness and Sq-Universality of Cyclically Presented Groups

Some group theoretic examples with completion theorem provers

Efficient finite groups arising in the study of relative asphericity

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