# Infinite groups with many generalized normal subgroups

Document Type: Research Paper

Authors

1 Dipartimento di Matematica e Applicazioni - University of Napoli Federico II

2 Universita di Napoli Federico II

Abstract

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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