A Möbius function is defined on the poset of element centers, producing new results about centralizers in p-groups.
Covering by Centralizers
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abstract
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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math.GR 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
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A M\"obius function on the centralizer lattice
A Möbius function is defined on the poset of element centers, producing new results about centralizers in p-groups.