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Algebra and Discrete Mathematics, 2005, Issue 1, Pages 69–83
(Mi adm290)
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This article is cited in 7 scientific papers (total in 7 papers)
RESEARCH ARTICLE
Abnormal subgroups and Carter subgroups in some infinite groups
L. A. Kurdachenkoa, I. Ya. Subbotinb a Mathematics Department, National Dnepropetrovsk University, Provylok Naukovyi 13, 49050 Dnepropetrovsk, Ukraine
b Mathematics Department, National
University, USA
Abstract:
Some properties of abnormal subgroups in generalized soluble groups are considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it is proven that a subgroup $H$ of a radical group G is abnormal in $G$ if and only if every intermediate subgroup for $H$ coincides with its normalizer in $G$. This result extends on radical groups the well-known criterion of abnormality for finite soluble groups due to D. Taunt. For some infinite groups (not only periodic) the existence of Carter subgroups and their conjugation have been also obtained.
Keywords:
abnormal subgroups, pronormal subgroups, Carter subgroups.
Received: 08.10.2004 Revised: 24.03.2005
Citation:
L. A. Kurdachenko, I. Ya. Subbotin, “Abnormal subgroups and Carter subgroups in some infinite groups”, Algebra Discrete Math., 2005, no. 1, 69–83
Linking options:
https://www.mathnet.ru/eng/adm290 https://www.mathnet.ru/eng/adm/y2005/i1/p69
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Abstract page: | 128 | Full-text PDF : | 57 | First page: | 1 |
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