## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Subgroup S-commutativity degrees of finite groups

#### Abstract

The so-called subgroup commutativity degree $sd(G)$ of a finite group $G$ is the number of permuting subgroups $(H,K) \in \mathrm{L}(G) \times \mathrm{L}(G)$, where $\mathrm{L}(G)$ is the subgroup lattice of $G$, divided by $|\mathrm{L}(G)|^2$. It allows to measure how $G$ is far from the celebrated classification of quasihamiltonian groups of K. Iwasawa. Here we generalize $sd(G)$, looking at suitable sublattices of $\mathrm{L}(G)$, and show some new lower bounds. More precisely, we define and study the subgroup S-commutativity degree of a group, which measures the probability that subnormal subgroups commute with maximal subgroups..

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 2 (2012), 373-382.

Dates
First available in Project Euclid: 24 May 2012

https://projecteuclid.org/euclid.bbms/1337864280

Mathematical Reviews number (MathSciNet)
MR2977239

Zentralblatt MATH identifier
1252.20025

Subjects
Primary: 06B23: Complete lattices, completions
Secondary: 20D60: Arithmetic and combinatorial problems

#### Citation

Otera, Daniele Ettore; Russo, Francesco G. Subgroup S-commutativity degrees of finite groups. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 2, 373--382. https://projecteuclid.org/euclid.bbms/1337864280