English

The non-$\mathfrak F$-graph of a finite group

Group Theory 2020-08-20 v1

Abstract

Given a formation F\mathfrak F, we consider the graph whose vertices are the elements of GG and where two vertices g,hGg,h\in G are adjacent if and only if g,hF\langle g,h \rangle \notin\mathfrak F. We are interested in the two following questions. Is the set of the isolated vertices of this graph a subgroup of GG? Is the subgraph obtained by deleting the isolated vertices a connected graph?

Keywords

Cite

@article{arxiv.2008.08455,
  title  = {The non-$\mathfrak F$-graph of a finite group},
  author = {Andrea Lucchini and Daniele Nemmi},
  journal= {arXiv preprint arXiv:2008.08455},
  year   = {2020}
}