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arXiv · 2008.08455

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

Andrea Lucchini·Daniele Nemmi
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Abstract

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

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Andrea Lucchini, Daniele Nemmi. 2020-08-19. The non-$\mathfrak F$-graph of a finite group. https://arxiv.org/abs/2008.08455

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