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Simultaneous conjugacy classes as combinatorial invariants of finite groups
Journal
Communications in Algebra
Date Issued
2022
Author(s)
Kaur D.
Indian Institute of Technology Jodhpur
Prajapati S.K.
Prasad A.
Abstract
We consider the problem of counting simultaneous conjugacy classes of n-tuples in a finite group G. Let (Formula presented.) denote the number of simultaneous conjugacy classes of n-tuples, and (Formula presented.) the number of simultaneous conjugacy classes of commuting n-tuples in G. We study the generating functions (Formula presented.) and (Formula presented.) which are rational functions of t. We show that (Formula presented.) determines and is completely determined by the class equation of G. We prove that the normalized functions (Formula presented.) and (Formula presented.) are invariants of isoclinism families. We compute exponential growth factors of (Formula presented.) and (Formula presented.). � 2022 Taylor & Francis Group, LLC.