Computing exterior isoclinism of crossed modules (Q6645111)

Isoclinism was introduced by \textit{P. Hall} [J. Reine Angew. Math. 182, 130--141 (1940; Zbl 0023.21001; JFM 66.0081.01)] as a classification of prime power groups. The notion of crossed module, generalizing the notion of a \(G\)-module, was introduced by \textit{J. H. C. Whitehead} [Ann. Math. (2) 49, 610--640 (1948; Zbl 0041.10102)] during his studies on the algebraic structure of the second relative homotopy group.\N\NThe authors introduce exterior isoclinism for crossed modules, extending the concept of isoclinism from groups to \(2\)-dimensional algebraic structures. Motivated by works on tensor and exterior products of non-abelian groups, they utilize non-abelian exterior products, exterior squares, and exterior centers to define a new equivalence relation. Additionally, the authors provide computational tools implemented in the GAP-system to identify exterior isoclinism families of small groups and crossed modules.