For symmetric groups, alternating groups, and finite simple classical groups of types A, B, and C, there always exists a non-trivial irreducible character of degree not divisible by two distinct primes that lies in both principal blocks.
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Character degrees in principal blocks for distinct primes
For symmetric groups, alternating groups, and finite simple classical groups of types A, B, and C, there always exists a non-trivial irreducible character of degree not divisible by two distinct primes that lies in both principal blocks.