Abstract
Let G be a finite group and write 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 2 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 PSL2(q) for q ⩾ 7.
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The second author was supported by the National Natural Science Foundation of China (11661042, 11471054 and 11761034).
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Lewis, M.L., Liu, Y. & Tong-Viet, H.P. Groups Satisfying the Two-Prime Hypothesis with a Composition Factor Isomorphic to PSL2(q) for q ⩾ 7. Czech Math J 68, 921–941 (2018). https://doi.org/10.21136/CMJ.2018.0027-17
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DOI: https://doi.org/10.21136/CMJ.2018.0027-17