Geodesic
Groups satisfying the two-prime hypothesis with a composition factor isomorphic to PSL$_2(q)$ for $q\geq 7$
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 921-941.

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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 $q \geq 7$.
DOI : 10.21136/CMJ.2018.0027-17
Classification : 20C15, 20D05
Keywords: character degrees; prime divisors 
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Lewis, Mark L.; Liu, Yanjun; Tong-Viet, Hung P. Groups satisfying the two-prime hypothesis with a composition factor isomorphic to PSL$_2(q)$ for $q\geq 7$. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 921-941. doi : 10.21136/CMJ.2018.0027-17. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0027-17/

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