Homomorphism Conjugacy versus Centralizer Actions in the Symmetric Group

2022/12/13 by Suleika Norrbom, Norrbom, Suleika
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Topics in Algebra #Chemical Synthesis and Analysis #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2212.06766

openalex publication_date 2022/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Homomorphisms of the alternating group A₅ into a reductive group
• The conjugacy action of S_n and modules induced from centralisers
• Conjugacy in Permutation Representations of the Symmetric Group
• Conjugacy problem for subgroups with applications to Artin groups and braid type groups
• Note on the conjugacy classes of elements and their centralizers for the free product of two groups