Derangements and Eigenvalue-Free Elements in Finite Classical Groups

DOI10.1112/S0024610798006772zbMath0936.15020OpenAlexW2130632424WikidataQ56988124 ScholiaQ56988124MaRDI QIDQ4265464

Peter M. Neumann, Cheryl E. Praeger

Publication date: 25 May 2000

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0024610798006772

zbMATH Keywords

random matricesfinite fieldfinite classical groupsderangementsmatrix ringeigenvalue-free elementsEuler's generating functions

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Random matrices (algebraic aspects) (15B52)

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Conditions for solvability in complex \(p\)-solvable linear groups. ⋮ Derangements in subspace actions of finite classical groups ⋮ Constructive recognition of classical groups in even characteristic. ⋮ Derangements in finite classical groups for actions related to extension field and imprimitive subgroups and the solution of the Boston–Shalev conjecture ⋮ A new faster algorithm for factoring skew polynomials over finite fields ⋮ Splitting fields for characteristic polynomials of matrices with entries in a finite field ⋮ A theorem on power series with applications to classical groups over finite fields ⋮ Convergence criteria for \(\text{FI}_{\mathcal{W}}\)-algebras and polynomial statistics on maximal tori in type B/C ⋮ The complexity of the weight problem for permutation and matrix groups. ⋮ Random matrix theory over finite fields ⋮ The Eulerian generating function of \(q\)-derangements ⋮ Finite simple unisingular groups of Lie type ⋮ Cyclic matrices in classical groups over finite fields ⋮ Some new results in random matrices over finite fields

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