A measuring argument for Schur rings
Abstract
Let G be a finite group and A a Schur ring over G. In this paper, we introduce the concept of lattice Schur rings and study their fundamental properties. For an A-subgroup H of G, we define the Schur Chermak-Delgado measure of H as Rank(AH)·|CG(H)|, where Rank(AH) denotes the rank of the subring AH⊆A, and CG(H) is the centralizer of H in G. Furthermore, we construct two families of finite groups and prove that the A-subgroups achieving the maximal Schur Chermak-Delgado measure form a sublattice in the subgroup lattice of G.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Combinatorial Mathematics
Advanced Topics in Algebra
Publication details
- Journal / source
- Communications in Algebra
- Pages
- 1–10
- Publication date
- 27 January 2026
- Language
- EN