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.
A generalization of groups with many almost normal subgroups
RUSSO, Francesco
Primo
2010-01-01
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.File in questo prodotto:
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