Geodesic
Periodic radical products of two locally nilpotent subgroups†
Glasgow mathematical journal, Tome 40 (1998) no. 2, pp. 241-255

Voir la notice de l'article provenant de la source Cambridge University Press

A group G is the product of its subgroups A and B if G equals the set AB = (ab | a ∊ A, b ∊ B). A subgroup H of G is called prefactorized if it is the product of a subgroup of A and a subgroup of B; thus H is prefactorized if and only if H = (H ∩ A)(H ∩ B). A prefactorized subgroup H of G is factorized if it contains A ∩ B. if H is any subgroup of G = AB, then the intersection X ofall factorized subgroups of G containing H is itself factorized; see for example [2, Lemma 1.1.2]. This subgroup, which is evidently the smallest factorized subgroup of G which contains H, is called the factorizer of H in G = AB. 
Höfling, Burkhard. Periodic radical products of two locally nilpotent subgroups†. Glasgow mathematical journal, Tome 40 (1998) no. 2, pp. 241-255. doi: 10.1017/S0017089500032560
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