The normal subgroup structure of ZM-groups
Marius Tarnauceanu
TL;DR
This paper investigates the structure and enumeration of normal subgroups within ZM-groups, providing criteria for when these subgroups form a chain, thereby enhancing understanding of their algebraic properties.
Contribution
It offers a complete characterization and counting method for normal subgroups of ZM-groups, including conditions for their chain formation.
Findings
Explicit enumeration of normal subgroups in ZM-groups
Necessary and sufficient conditions for normal subgroups to form a chain
Enhanced understanding of the subgroup lattice structure
Abstract
The main goal of this note is to determine and to count the normal subgroups of a ZM-group. We also indicate some necessary and sufficient conditions such that the normal subgroups of a ZM-group form a chain.
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