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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2010, Volume 9, Issue 1, Pages 79–85 (Mi adm21)

RESEARCH ARTICLE

A generalization of groups with many almost normal subgroups

Francesco G. Russo

Department of Mathematics, University of Naples Federico II, via Cinthia I-80126, Naples, Italy

Abstract: A subgroup $H$ of a group $G$ is called almost normal in $G$ if it has finitely many conjugates in $G$. A classic result of B. H. Neumann informs us that $|G:\mathbf{Z}(G)|$ is finite if and only if each $H$ is almost normal in $G$. Starting from this result, we investigate the structure of a group in which each non-finitely generated subgroup satisfies a property, which is weaker to be almost normal.

Keywords: Dietzmann classes; anti-$\mathfrak{X}C$-groups; groups with $\mathfrak{X}$-classes of conjugate subgroups; Chernikov groups.

Full text: PDF file (203 kB)

Bibliographic databases:
MSC: 20C07, 20D10, 20F24
Revised: 25.02.2010
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Citation: Francesco G. Russo, “A generalization of groups with many almost normal subgroups”, Algebra Discrete Math., 9:1 (2010), 79–85

Citation in format AMSBIB
\Bibitem{Rus10} \by Francesco G. Russo \paper A generalization of groups with many almost normal subgroups \jour Algebra Discrete Math. \yr 2010 \vol 9 \issue 1 \pages 79--85 \mathnet{http://mi.mathnet.ru/adm21} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2676713} \zmath{https://zbmath.org/?q=an:1209.20025}