On finite products of nilpotent groups
Bernhard Amberg1994, Archiv der Mathematik
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Abstract
i. Introduetion. A well-known theorem of Kegel [7] and Wielandt [9] states the solubility of every finite group G = AB which is the product of two nilpotent subgroups A and B; see [1], Theorem 2.4.3. In order to determine the structure of these groups it is of interest to know which subgroups of G are conjugate (or at least isomorphic) to a subgroup that inherits the factorization. A subgroup S of the factorized group G = AB is called prefactorized if S = (A c~ S) (B ~ S), it is called factorized if, in addition, S contains the intersection A c~ B. Generally, even characteristic subgroups of G are not prefactorized, as can be seen e.g. from Examples 1 and 2 below.
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