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Suleika Norrbom: Bevis: Homomorphism Conjugacy versus Centralizer Actions

Time: Fri 2022-02-11 11.30 - 12.30

Location: Zoom

Video link: 611 0261 0226, contact to get the password

Respondent: Suleika Norrbom

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Abstract: We explore local versus global conjugacy of homomorphisms in relation to actions induced by centralizers in the target group. Our focus is the case where the source group is abelian and the target group is the symmetric group. It is shown that understanding centralizers in the symmetric group enables us to determine when such homomorphisms are conjugate in some special cases. We also further our understanding of centralizers in the symmetric group by looking at homomorphisms with abelian source groups. This highlights that our results create a foundation and incentive for studying local versus global conjugacy in the symmetric group for more complicated source groups.