Mohamed, Esamaldeen and Williams, Gerald (2023) Counting isomorphism classes of groups of Fibonacci type with a prime power number of generators. Journal of Algebra, 633. pp. 887-905. DOI https://doi.org/10.1016/j.jalgebra.2023.04.032
Mohamed, Esamaldeen and Williams, Gerald (2023) Counting isomorphism classes of groups of Fibonacci type with a prime power number of generators. Journal of Algebra, 633. pp. 887-905. DOI https://doi.org/10.1016/j.jalgebra.2023.04.032
Mohamed, Esamaldeen and Williams, Gerald (2023) Counting isomorphism classes of groups of Fibonacci type with a prime power number of generators. Journal of Algebra, 633. pp. 887-905. DOI https://doi.org/10.1016/j.jalgebra.2023.04.032
Abstract
Cavicchioli, O'Brien, and Spaggiari studied the number of isomorphism classes of irreducible groups of Fibonacci type as a function σ(n) of the number of generators n. In the case n=pl, where p is prime and l≥1, n≠2,4, they conjectured a function C(pl), that is polynomial in p, for the value of σ(pl). We prove that C(pl) is an upper bound for σ(pl). We introduce a function τ(n) for the number of abelianised groups and conjecture a function D(pl), that is polynomial in p, for the value of τ(pl), when pl≠2,4,5,7,8,13,23. We prove that D(pl) is an upper bound for τ(pl). We pose three questions that ask if particular pairs of groups with common abelianisations are non-isomorphic. We prove that if τ(pl)=D(pl) and each of these questions has a positive answer then σ(pl)=C(pl).
Item Type: | Article |
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Uncontrolled Keywords: | Cyclically presented group; Fibonacci group; Isomorphism |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 02 Aug 2023 19:51 |
Last Modified: | 30 Oct 2024 21:21 |
URI: | http://repository.essex.ac.uk/id/eprint/36112 |
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