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arXiv · 2411.19837

The connectivity of the normalising and permuting graph of a finite soluble group

Eoghan Farrell·Chris Parker
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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.

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Eoghan Farrell, Chris Parker. 2024-11-29. The connectivity of the normalising and permuting graph of a finite soluble group. https://arxiv.org/abs/2411.19837

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