Thompson's character-degree normal complement theorem
= Thompson's character-degree normal complement theorem
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If a prime $p$ divides the degree of every <nonlinear irreducible character> of a finite group, the group has a <normal p-complement>. Indeed, the p-prime-degree characters are exactly the linear characters. Their squared-degree sum is $|G:G'|$, whose p-part is $|G:G'|_p$; <Isaacs' character-degree criterion for p-nilpotency> applies.