Derangements in wreath products of permutation groups

Vishnuram Arumugam, Heiko Dietrich, S. P. Glasby

Research output: Contribution to journalArticlepeer-review

Abstract

Given a finite group G acting on a set X let δk(G, X) denote the proportion of elements in G that have exactly k fixed points in X. Let Sn denote the symmetric group acting on [n] = { 1 , 2 , ⋯ , n} . For A⩽ Sm and B⩽ Sn , the permutational wreath product A≀ B has two natural actions and we give formulas for both, δk(A≀ B, [m] × [n]) and δk(A≀ B, [m] [n]) . We prove that for k= 0 the values of these proportions are dense in the intervals [δ(B, [n]) , 1] and [δ(A, [m]) , 1] . Among further results, we provide estimates for δ(G, [m] [n]) for subgroups G⩽ Sm≀ Sn containing Am[n] .

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalJournal of Algebraic Combinatorics
Volume59
Issue number1
Early online date28 Aug 2023
DOIs
Publication statusPublished - Jan 2024

Cite this