The Chermak-Delgado Measure as a Map on Posets
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913229362429952 |
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| author | Cocke, William McCulloch, Ryan |
| author_facet | Cocke, William McCulloch, Ryan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Chermak-Delgado Measure as a Map on Posets Cocke, William McCulloch, Ryan Group Theory Primary 20D30, 20E15 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. |
| title | The Chermak-Delgado Measure as a Map on Posets |
| topic | Group Theory Primary 20D30, 20E15 |
| url | https://arxiv.org/abs/2401.12450 |