A generalization of groups with many almost normal subgroups

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    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 $|G : Z(G)|$ 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.
    Lingua originaleEnglish
    pagine (da-a)79-85
    Numero di pagine7
    RivistaAlgebra and Discrete Mathematics
    Volume9
    Stato di pubblicazionePublished - 2010

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    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 $|G : Z(G)|$ 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.",
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    journal = "Algebra and Discrete Mathematics",
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    N2 - 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 $|G : Z(G)|$ 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.

    AB - 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 $|G : Z(G)|$ 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.

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

    UR - http://hdl.handle.net/10447/55671

    UR - http://adm.lnpu.edu.ua/

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    JO - Algebra and Discrete Mathematics

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    SN - 1726-3255

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