Energetic formulation of the subgroup commutativity degree
Abstract
Finite groups in which every pair of subgroups (H, K) satisfies H K = K H have been classified by Iwasawa, but only in the last decade it was introduced the notion of subgroup commutativity degree sd(G) of groups G. From restrictions of numerical nature on sd(G) one usually derives structural conditions on G; in fact, among groups G with sd(G) = 1, one finds those originally studied by Iwasawa. Here we offer a new perspective of study for sd(G); we use a recently introduced graph, which is called nonpermutability graph of subgroups ΓL(G) of G, in order to restrict sd(G) via the notion of energy of ΓL(G) and by means of methods of spectral graph theory. In particular, we find new criteria of nilpotence for G along with new bounds for sd(G).
Fields of Study & Subjects
Finite Group Theory Research
Advanced Operator Algebra Research
Rings
Modules
and Algebras
Publication details
- Journal / source
- Nonlinear Analysis Modelling and Control
- Volume
- 31
- Issue
- 1
- Pages
- 212–236
- Publication date
- 1 January 2026
- Language
- EN