Computing 3-dimensional groups: Crossed squares and cat2-groups

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ARVASİ Z., Odabas A., Wensley C. D.

JOURNAL OF SYMBOLIC COMPUTATION, vol.114, pp.267-281, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 114
  • Publication Date: 2023
  • Doi Number: 10.1016/j.jsc.2022.04.020
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.267-281
  • Keywords: Cat(2) -group, Crossed square, GAP, XMod, ALGEBRAIC MODELS, HOMOTOPY, MODULES, SPACES
  • Eskisehir Osmangazi University Affiliated: Yes


The category XSq of crossed squares is equivalent to the category Cat2 of cat(2)-groups. Functions for computing with these structures have been developed in the package XMod written using the GAP computational discrete algebra programming language. This paper contains a table listing the numbers iota(2)(G)& nbsp;of isomorphism classes of cat(2)-groups on groups G of order at most 30 - a total of 1007 cat(2)- groups. Secondly, it contains general formulae for iota(2)(G) in a number of special cases. (C)& nbsp;2022 Elsevier Ltd. All rights reserved.