Given a formation (Formula presented.), we consider the graph whose vertices are the elements of G and where two vertices (Formula presented.) are adjacent if and only if (Formula presented.). 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?.
The non-F graph of a finite group
Lucchini A.;Nemmi D.
2021
Abstract
Given a formation (Formula presented.), we consider the graph whose vertices are the elements of G and where two vertices (Formula presented.) are adjacent if and only if (Formula presented.). 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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