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Groups in which the prime graph is a tree

Maria Silvia Lucido — 2002

Bollettino dell'Unione Matematica Italiana

The prime graph Γ G of a finite group G is defined as follows: the set of vertices is π G , the set of primes dividing the order of G , and two vertices p , q are joined by an edge (we write p q ) if and only if there exists an element in G of order p q . We study the groups G such that the prime graph Γ G is a tree, proving that, in this case, π G 8 .

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