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Elliptically Embedded Subgroups of Polycyclic Groups

A subgroup H of a group G is elliptically embedded in G if for each subgroup K of G there is an integer n = n(K) such that$\langle H, K \rangle = HK \cdots HK$, where the product has 2n factors. It is shown that a subgroup H of a polycyclic by finite group G is elliptically embedded in G if and only...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1988, Vol.102 (2), p.230-234
Main Authors: Rhemtulla, A. H., Wilson, J. S.
Format: Article
Language:English
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Summary:A subgroup H of a group G is elliptically embedded in G if for each subgroup K of G there is an integer n = n(K) such that$\langle H, K \rangle = HK \cdots HK$, where the product has 2n factors. It is shown that a subgroup H of a polycyclic by finite group G is elliptically embedded in G if and only if H is subnormal in some subgroup of finite index in G.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1988-0920978-1