Homomorphism Conjugacy versus Centralizer Actions in the Symmetric Group
Suleika Norrbom
TL;DR
This paper investigates conditions under which certain homomorphisms from abelian or dihedral groups to the symmetric group are conjugate, focusing on generator-conjugate and element-conjugate cases, with a complete classification for two-generator sources.
Contribution
It provides a complete characterization of conjugacy conditions for homomorphisms from two-generator groups to the symmetric group, based on centralizer actions.
Findings
Generator-conjugate homomorphisms are conjugate under specific conditions.
Element-conjugate homomorphisms are conjugate in certain cases.
Classification is complete for two-generator source groups.
Abstract
We explore when generator-conjugate homomorphisms are conjugate and when element-conjugate homomorphisms are conjugate from abelian or dihedral groups to the symmetric group. We completely determine when such homomorphisms are conjugate in the case where the source group has two generators by studying centralizer actions in the target group.
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Taxonomy
TopicsChemical Synthesis and Analysis · Advanced Topics in Algebra · Rings, Modules, and Algebras