Intersections of Sylow 2-subgroups in symmetric groups
Sean Eberhard

TL;DR
This paper calculates the asymptotic probability that two random Sylow 2-subgroups in symmetric and alternating groups intersect trivially, providing insights into subgroup interactions in large symmetric groups.
Contribution
It offers the first asymptotic probability computation for trivial intersection of Sylow 2-subgroups in symmetric and alternating groups, complementing recent related research.
Findings
Asymptotic probability of trivial intersection approaches a specific limit
Provides explicit formulas for symmetric and alternating groups
Enhances understanding of subgroup structure in large groups
Abstract
We compute the asymptotic probability that a random pair of Sylow 2-subgroups in or intersects trivially. This calculation complements recent work of Diaconis, Giannelli, Guralnick, Law, Navarro, Sambale, and Spink (see arXiv:2504.01149).
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