Year: 2025
Type: article
Abstract: We introduce the normalizing graph of a group and study the connectivity of the normalizing and permuting graphs of a group when the group is finite and soluble. In particular, we classify finite soluble groups with disconnected normalizing graph. The main results shows that if a finite soluble group has connected normalizing graph then this graph has diameter at most 6. Furthermore, this bound is tight. A corollary then presents the connectivity properties of the permuting graph.
Source: Communications in Algebra
Authors: Eoghan Farrell, Chris Parker
Institution: University of Birmingham
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4407136311