The generating graph Λ(H) of a finite group H is the graph defined on the elements of H, with an edge between two vertices if and only if they generate H. We show that if H is a sufficiently large simple group with Λ (G) ∼ Λ (H) for a finite group G, then G ∼ H. We also prove that the generating graph of a symmetric group determines the group.
ON the GENERATING GRAPH of A SIMPLE GROUP
LUCCHINI, ANDREA;
2017
Abstract
The generating graph Λ(H) of a finite group H is the graph defined on the elements of H, with an edge between two vertices if and only if they generate H. We show that if H is a sufficiently large simple group with Λ (G) ∼ Λ (H) for a finite group G, then G ∼ H. We also prove that the generating graph of a symmetric group determines the group.File in questo prodotto:
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