### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 79-85 |

Numero di pagine | 7 |

Rivista | Algebra and Discrete Mathematics |

Volume | 9 |

Stato di pubblicazione | Published - 2010 |

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**A generalization of groups with many almost normal subgroups.** / Russo, Francesco.

Risultato della ricerca: Article

*Algebra and Discrete Mathematics*, vol. 9, pagg. 79-85.

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TY - JOUR

T1 - A generalization of groups with many almost normal subgroups

AU - Russo, Francesco

PY - 2010

Y1 - 2010

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/

M3 - Article

VL - 9

SP - 79

EP - 85

JO - Algebra and Discrete Mathematics

JF - Algebra and Discrete Mathematics

SN - 1726-3255

ER -