The Prime Graph of a Sporadic Simple Group
By Mina Hagie. 2003
90 citations recorded by the source corpus.
Abstract Let Gbe a finite group and Sa sporadic simple group. We denote by π(G) the set of all primes dividing the order of G. The prime graph Γ(G) of Gis defined in the usual way connecting pand qin π(G) when there is an element of order pqin G. The main purpose of this paper is to determine finite group Gsatisfying Γ(G) = Γ(S) (See Theorem 3) and to give applications which generalize Abe (Abe, S. Two ways to characterize 26 sporadic finite simple groups. Preprint) and Chen (Chen, G. (1996). A new characterization of sporadic simple groups. Algebra Colloq.3:49–58). The results are elementary but quite useful.
Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/d416fa2527ac6b80f055ee4ceec61cc87e1c12de
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
In Discrete Mathematics and Combinatorics
In Electrical and Electronic Engineering
Citations in the corpus
- Recognition of finite groups by the prime graph (2006, methodology): “After this article had been submitted, I became aware of the paper [ 19 ] in which part of Theorem C was proven: if G is a finite group with the same prime graph as for the Monster M then G/O3(G) ∼ M .”