Demonstrates maximal and minimal covers of finite groups by centralizers, indicating significant group properties.
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 .
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Lewis et al. (2026) studied this question.
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