2020/08/28 by Giovanni De Franceschi, De Franceschi, Giovanni
Mathematics · Computer Science · #Finite Group Theory Research #Coding theory and cryptography #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2008.12651
Let \mathscrC be a classical group defined over a finite field. We present comprehensive theoretical solutions to the following closely related problems: 1) List a representative for each conjugacy class of \mathscrC. 2) Given x ∈ \mathscrC, describe the centralizer C_\mathscrC(x) of x in \mathscrC, by giving its group structure and a generating set. 3) Given x,y ∈ \mathscrC, establish whether x and y are conjugate in \mathscrC and, if they are, find explicit z ∈ \mathscrC such that z-1xz = y. We also formulate practical algorithms to solve these problems and have implemented them in Magma.