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math.GR2025
Derangements in finite classical groups and characteristic polynomials of random matrices
Jason Fulman, Robert Guralnick
We first obtain explicit upper bounds for the proportion of elements in a finite classical group G with a given characteristic polynomial. We use this to complete the proof that th…
math.GR2025
Commuting probability for conjugate subgroups of a finite group
Eloisa Detomi, Robert M. Guralnick, Marta Morigi +1
Given two subgroups H,K of a finite group G, the probability that a pair of random elements from H and K commutes is denoted by \pr(H,K). We address the following question. Let P b…