construct the Gruenberg-Kegel graph of a group
GruenbergKegelGraph( G )
a small group
For a finite group G, the Gruenberg-Kegel graph (also known as the prime graph) of G is the graph with vertices the prime divisors of the order of G, and for which two vertices p and q are adjacent if G has an element of order pq.
The GruenbergKegelGraph( 'G' ) command returns the Gruenberg-Kegel graph of the finite group G.
Commands in the GraphTheory package can be used to visualize the graph returned by this command, as well as to analyze its properties.
The vertices of the Gruenberg-Kegel graph of the Monster sporadic finite simple group are the so-called supersingular primes.
GKG ≔ GruenbergKegelGraph⁡Monster⁡
GKG≔Graph 1: an undirected graph with 15 vertices, 23 edge(s), and 3 self-loop(s)
The self-loops indicate those supersingular primes p for which the Monster has an element of order p2.
The Gruenberg-Kegel graph of a Frobenius group is never connected.
G ≔ FrobeniusGroup⁡2238,1:
GKG ≔ GruenbergKegelGraph⁡G
GKG≔Graph 2: an undirected graph with 3 vertices and 1 edge(s)
The GroupTheory[GruenbergKegelGraph] command was introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
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