For a finite group G, let Gamma(G) denote the graph defined on the non-identity elements of G in such a way that two distinct vertices are connected by an edge if and only if they generate G. We prove that if G is soluble, then the non-isolated vertices of Gamma(G) belong to a unique connected component.
The generating graph of finite soluble groups
CRESTANI, ELEONORA;LUCCHINI, ANDREA
2013
Abstract
For a finite group G, let Gamma(G) denote the graph defined on the non-identity elements of G in such a way that two distinct vertices are connected by an edge if and only if they generate G. We prove that if G is soluble, then the non-isolated vertices of Gamma(G) belong to a unique connected component.File in questo prodotto:
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