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arXiv · 2401.12450

The Chermak-Delgado Measure as a Map on Posets

William Cocke·Ryan McCulloch
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Abstract

The Chermak-Delgado measure of a finite group is a function which assigns to each subgroup a positive integer. In this paper, we give necessary and sufficient conditions for when the Chermak-Delgado measure of a group is actually a map of posets, i.e., a monotone function from the subgroup lattice to the positive integers. We also investigate when the Chermak-Delgado measure, restricted to the centralizers, is increasing.

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William Cocke, Ryan McCulloch. 2024-01-23. The Chermak-Delgado Measure as a Map on Posets. https://arxiv.org/abs/2401.12450

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