Permutizer

noun

noun ·Rare ·Advanced level

Definitions

Noun
  1. 1
    A subgroup of all cyclic subgroups that permute with another

    "Given a finite group G, we introduce the \textit{permutability degree} of G, as Gwhere\mathcal{L}(G)isthesubgrouplatticeofGandP_G(X)thepermutizerofthesubgroupXinG,thatis,thesubgroupgeneratedbyallcyclicsubgroupsofGthatpermutewithX\in \mathcal{L}(G)$."

Example

More examples

"Given a finite group G, we introduce the \textit{permutability degree} of G, as Gwhere\mathcal{L}(G)isthesubgrouplatticeofGandP_G(X)thepermutizerofthesubgroupXinG,thatis,thesubgroupgeneratedbyallcyclicsubgroupsofGthatpermutewithX\in \mathcal{L}(G)$."

Etymology

From permute + -izer.

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.