Infinite groups with many generalized normal subgroups

Infinite groups with many generalized normal subgroups

A subgroup $X$ of a group $G$ is almost normal if the index $|G:N_G(X)|$ is finite, while $X$ is nearly normal if it has finite index in the normal closure $X^G$. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.

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Veröffentlicht in:International journal of group theory 2012-09, Vol.1 (3), p.39-49
Hauptverfasser: Francesco de Giovanni, Caterina Rainone
Format: Artikel
Sprache:eng
Schlagworte:
Almost normality
nearly normality
normalizer subgroup
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Zusammenfassung:A subgroup $X$ of a group $G$ is almost normal if the index $|G:N_G(X)|$ is finite, while $X$ is nearly normal if it has finite index in the normal closure $X^G$. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.
ISSN:2251-7650
2251-7669