Subgroups of locally finite products of locally nilpotent groups

Research Report MRR97-005

Subgroups of locally finite products of locally nilpotent groups

Burkhard Höfling

Abstract: Let the locally finite group G be the product of two locally nilpotent subgroups A and B, and assume that H is a subgroup of G belonging to a group class $\frak F$ . The question is considered whether there exists a subgroup X of G containing H which belongs to $\frak F$ and satisfies $X = (X \cap A)(X \cap B)$ . Under various assumptions on G and $\frak F$ , necessary and sufficient conditions for the existence of such a subgroup X are obtained.

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