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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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Published in: | Proceedings of the American Mathematical Society 1988, Vol.102 (2), p.230-234 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0002-9939 1088-6826 |
DOI: | 10.1090/S0002-9939-1988-0920978-1 |