Isoclinism of groups

In mathematics, specifically group theory, isoclinism is an equivalence relation on groups which generalizes isomorphism. Isoclinism was introduced by Hall (1940) to help classify and understand p-groups, although it is applicable to all groups. Isoclinism also has consequences for the Schur multiplier and the associated aspects of character theory, as described in Suzuki (1982, p. 256) and Conway et al. (1985, p. xxiii, Ch. 6.7). The word "isoclinism" comes from the Greek ισοκλινης meaning equal slope.