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

2020/08/19 by Lucchini, Andrea, Nemmi, Daniele
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2008.08455

Abstract

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

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