The Chermak-Delgado lattice of ZM-groups
Marius T\u{a}rn\u{a}uceanu
TL;DR
This paper investigates the Chermak-Delgado lattice structure of ZM-groups and certain dihedral groups, revealing that these lattices are chains of length zero, indicating minimal complexity in their subgroup organization.
Contribution
It proves that the Chermak-Delgado lattice of ZM-groups is a chain of length zero and extends this result to dihedral groups D_{2m} with m ≠ 4.
Findings
Chermak-Delgado lattice of ZM-groups is a chain of length zero
Similar lattice structure found in dihedral groups D_{2m} for m ≠ 4
Lattice simplicity indicates minimal subgroup complexity
Abstract
In this note we prove that the Chermak-Delgado lattice of a ZM-group is a chain of length . A similar conclusion is obtained for all dihedral groups with .
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Taxonomy
TopicsFinite Group Theory Research · Geometric and Algebraic Topology · Mathematical Dynamics and Fractals