Covering by Centralizers
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913011063586816 |
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| author | Lewis, Mark L. McCulloch, Ryan |
| author_facet | Lewis, Mark L. McCulloch, Ryan |
| contents | In this paper, we consider covers of finite groups by centralizers of elements. We show that the set of centralizers that are maximal under the partial ordering form a cover of the group. We also show that the set of centralizers that are minimal under the partial ordering form a cover of the group. We show for $F$-groups that are nonabelian $p$-groups that the number of distinct nontrivial centralizers is congruent to $1$ modulo $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02211 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Covering by Centralizers Lewis, Mark L. McCulloch, Ryan Group Theory Primary 20D99, Secondary 05C25 In this paper, we consider covers of finite groups by centralizers of elements. We show that the set of centralizers that are maximal under the partial ordering form a cover of the group. We also show that the set of centralizers that are minimal under the partial ordering form a cover of the group. We show for $F$-groups that are nonabelian $p$-groups that the number of distinct nontrivial centralizers is congruent to $1$ modulo $p$. |
| title | Covering by Centralizers |
| topic | Group Theory Primary 20D99, Secondary 05C25 |
| url | https://arxiv.org/abs/2512.02211 |