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arXiv · 2206.12758

Central Products and the Chermak-Delgado Lattice

William Cocke·Ryan McCulloch
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Abstract

The Chermak-Delgado lattice of a finite group is a modular, self-dual sublattice of the lattice of subgroups. We prove that the Chermak-Delgado lattice of a central product contains the product of the Chermak-Delgado lattices of the relevant central factors. Furthermore, we obtain information about heights of elements in the Chermak-Delgado lattice relative to their heights in the Chermak-Delgado lattices of central factors. We also explore how the central product can be used as a tool in investigating Chermak-Delgado lattices.

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William Cocke, Ryan McCulloch. 2022-06-26. Central Products and the Chermak-Delgado Lattice. https://doi.org/10.1016/j.jpaa.2024.107769

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