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...A|3, |B|3} > |G|. (1) This motivates the following definition. Definition 1. Let G be a finite group. A proper subgroup H of G is said to be large if the order of H satisfies the bound |H|3 > |G|. In =-=[2]-=-, Alavi and Praeger develop a general framework for studying triple factorisations of finite groups in terms of group actions. In particular, a reduction strategy for classifying triple factorisations...

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...ur for a wide range of possible parameters (e.g., dimension, cardinality of F). Apart from the role that such factorisations have in linear algebra or in the theory of groups (see the Introduction of =-=[3]-=-), there is also an interesting connection with incidence geometry, whereby the study of flag-transitive point/line geometries involves the study of triple factorisations of their automorphism groups....