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Keywords:
character degrees; prime divisors
character degrees; prime divisors
Summary:
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 $q \geq 7$.
References:
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