On the subgroup permutability degree of the simple Suzuki groups

TL;DR

This paper demonstrates that as the size of simple Suzuki groups increases, the likelihood of a subgroup being permutable approaches zero, while almost all subgroups tend to be 2-groups.

Contribution

It establishes the asymptotic behavior of the subgroup permutability degree in simple Suzuki groups and the probability that a subgroup is a 2-group.

Findings

Subgroup permutability degree vanishes asymptotically.

Probability of a subgroup being a 2-group tends to 1.

Provides new insights into subgroup structure of Suzuki groups.

Abstract

We prove that the subgroup permutability degree of the simple Suzuki groups vanishes asymptotically. In the course of the proof we establish that the limit of the probability of a subgroup of $\Sz(q)$ being a 2-group is equal to 1.