Abstract
We introduce the normalising graph of a group and study the connectivity of the normalising and permuting graphs of a group when the group is finite and soluble. In particular, we classify finite soluble groups with disconnected normalising graph. The main results shows that if a finite soluble group has connected normalising 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.
| Original language | English |
|---|---|
| Pages (from-to) | 3134–3143 |
| Number of pages | 10 |
| Journal | Communications in Algebra |
| Volume | 53 |
| Issue number | 8 |
| Early online date | 4 Feb 2025 |
| DOIs | |
| Publication status | Published - 4 Feb 2025 |
Bibliographical note
Copyright:© 2025 The Author(s). Published with license by Taylor & Francis Group, LLC.
Keywords
- commuting graphs
- connectivity
- Finite soluble groups
- permuting and normalising graph
ASJC Scopus subject areas
- Algebra and Number Theory
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