Perfect Prishchepov groups

[摘要] 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. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-15

[关键词] Prishchepov groups;Cyclically presented groups;Perfect groups;LOG groups