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Periodic radical products of two locally nilpotent subgroups†

Published online by Cambridge University Press:  18 May 2009

Burkhard Höfling
Burkhard Höfling
Affiliation:
School of Mathematical Sciences, Australian National University, Canberra Act 0200, Australia
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 2 , May 1998 , pp. 241 - 255
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

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