Francesco de Giovanni, Carmela Musella
Abstract
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A subgroup $H$ of a group $G$ is nearly normal if it has finite index in its normal closure $H^G$. A relevant theorem of B. H. Neumann states that groups in which every subgroup is nearly normal are precisely those with finite commutator subgroup.
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A subgroup $H$ of a group $G$ is nearly normal if it has finite index in its normal closure $H^G$. A relevant theorem of B. H. Neumann states that groups in which every subgroup is nearly normal are precisely those with finite commutator subgroup.
Key concepts: Mathematics, Commutator subgroup, Characteristic subgroup, Normal subgroup, Fitting subgroup, Index of a subgroup, Maximal subgroup, Modular group