Year: 2021
Type: article
Abstract: We study random generation in the symmetric group when cycle type restrictions are imposed. Given π , π ′ ∈ S n , we prove that π and a random conjugate of π ′ are likely to generate at least A n provided only that π and π ′ have not too many fixed points and not too many 2 -cycles. As an application, we investigate the following question: For which positive integers m should we expect two random elements of order m to generate A n ? Among other things, we give a positive answer for any m having any divisor d in the range 3 ≤ d ≤ o ( n 1 / 2 ) .
Source: Algebraic Combinatorics
DOI: 10.5802/alco.149
Authors: Sean Eberhard, Daniele Garzoni
Language: Latvian
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2940569701