$${\varvec{z}}$$ z -classes in groups: a survey

Sushil Bhunia and Anupam Singh
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Sushil Bhunia: IISER Mohali
Anupam Singh: IISER Pune

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 3, 713-720

Abstract: Abstract This survey article explores the notion of z-classes in groups. The concept introduced here is related to the notion of orbit types in transformation groups, and types or genus in the representation theory of finite groups of Lie type. Two elements in a group are said to be z-equivalent (or z-conjugate) if their centralizers are conjugate. This is a weaker notion than the conjugacy of elements. In this survey article, we present several known results on this topic and suggest some further questions.

Keywords: z-classes; Groups; Classical groups; Glgebraic groups; 20G40; 05A15; 20E45 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00186-6

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