2024/10/28 by Thomas Michael Keller, Keller, Thomas Michael, Zachary Martin +7
Mathematics · Engineering · #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2410.21063
For a finite group G, the vertices of the prime graph Γ(G) are the primes that divide |G|, and two vertices p and q are connected by an edge if there is an element of order pq in G. Prime graphs of solvable groups have been classified, and prime graphs of groups whose noncyclic composition factors are isomorphic to a single nonabelian simple group T have been classified in the case where T has order divisible by exactly three or four distinct primes, except for the cases T = Sz(8), T = Sz(32), and T = PSL(2,q), which in some sense are the hardest cases. In this paper, we complete the classification for T = Sz(32), T = Sz(8), and T = PSL(2,25), with the latter two being the first cases ever studied where |Out(T)| has prime factors which do not divide |T|. The groups studied in this paper are also the first ones requiring knowledge of their Brauer character tables to complete the classification task.