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Algebra and Discrete Mathematics, 2012, Volume 14, Issue 1, Pages 84–106
(Mi adm86)
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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
Groups with many pronormal and transitively normal subgroups
L. A. Kurdachenkoa, N. N. Semko (Jr.)b, I. Ya. Subbotinc a Department of Algebra, National University of Dnepropetrovsk, Vul. Naukova 13, Dnepropetrovsk 50, Ukraine 49050
b Department of Mathematics, National University of The State Tax Service of Ukraine, Irpen, Ukraine
c Department of Mathematics and Natural Sciences, National University, 5245 Pacific Concourse Drive, LA, CA 90045, USA
Abstract:
A subgroup H of a group G is said to be transitively normal in G, if H is normal in every subgroup K⩾H such that H is subnormal in K. We described some infinite groups, whose non–finitely generated subgroups are transitively normal.
Keywords:
soluble group, radical group, locally nilpotent group, transitively normal subgroup, non finitely generated subgroup.
Received: 29.05.2012 Accepted: 29.05.2012
Citation:
L. A. Kurdachenko, N. N. Semko (Jr.), I. Ya. Subbotin, “Groups with many pronormal and transitively normal subgroups”, Algebra Discrete Math., 14:1 (2012), 84–106
Linking options:
https://www.mathnet.ru/eng/adm86 https://www.mathnet.ru/eng/adm/v14/i1/p84
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Abstract page: | 313 | Full-text PDF : | 103 | References: | 61 | First page: | 1 |
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