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Perfect Prishchepov Groups

Chinyere, Ihechukwu and Bainson, Bernard (2021) 'Perfect Prishchepov Groups.' Journal of Algebra, 588. pp. 515-532. ISSN 0021-8693

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We study cyclically presented groups of type F to determine when they are perfect. It turns out that to do so, it is enough to consider the Prishchepov groups, so modulo a certain conjecture, we classify the perfect Prishchepov groups P(r, n, k, s, q) in terms of the defining integer parameters r, n, k, s, q. In particular, we obtain a classification of the perfect Campbell and Robertson’s Fibonacci-type groups H(r, n, s), thereby proving a conjecture of Williams, and yielding a complete classification of the groups H(r, n, s) that are connected Labelled Oriented Graph groups.

Item Type: Article
Uncontrolled Keywords: Prishchepov groups; Cyclically presented groups; Perfect groups; LOG groups
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 20 Sep 2021 08:56
Last Modified: 09 Sep 2022 01:00

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