Czechoslovak Mathematical Journal, Vol. 68, No. 4, pp. 921-941, 2018
Groups satisfying the two-prime hypothesis with a composition factor isomorphic to PSL$_2(q)$ for $q\geq7$
Mark L. Lewis, Yanjun Liu, Hung P. Tong-Viet
Received January 19, 2017. Published online June 8, 2018.
Abstract: Let $G$ be a finite group and write ${\rm cd} (G)$ for the degree set of the complex irreducible characters of $G$. The group $G$ is said to satisfy the two-prime hypothesis if for any distinct degrees $a, b \in{\rm cd} (G)$, the total number of (not necessarily different) primes of the greatest common divisor $\gcd(a, b)$ is at most $2$. We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL$_2 (q)$ for $q \geq7$.
Affiliations: Mark L. Lewis, Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA, e-mail: lewis@math.kent.edu; Yanjun Liu, College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, P.R. China, e-mail: liuyanjun@pku.edu.cn; Hung P. Tong-Viet, Department of Mathematical Sciences, Binghamton University, 4400 Vestal Parkway East, Binghamton, NY 13902-6000, USA, e-mail: tongviet@math.binghamton.edu
