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<p>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 <i>F</i>-groups that are nonabelian <i>p</i>-groups that the number of distinct nontrivial centralizers is congruent to 1 modulo <i>p</i>.</p>

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Covering by Centralizers

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月17日

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  • Mark L. Lewis,
  • Ryan McCulloch

摘要

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.