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Proceedings of the American Mathematical Society

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Elliptically embedded subgroups of polycyclic groups


Authors: A. H. Rhemtulla and J. S. Wilson
Journal: Proc. Amer. Math. Soc. 102 (1988), 230-234
MSC: Primary 20E15,; Secondary 20F16
DOI: https://doi.org/10.1090/S0002-9939-1988-0920978-1
MathSciNet review: 920978
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Abstract: 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 $ \left\langle {H,K} \right\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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DOI: https://doi.org/10.1090/S0002-9939-1988-0920978-1
Keywords: Polycyclic groups, subnormal subgroups
Article copyright: © Copyright 1988 American Mathematical Society

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