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Groups with few $$p'$$-character degrees. (English) Zbl 07187749
Summary: We prove a variation of Thompson’s Theorem. Namely, if the first column of the character table of a finite group $$G$$ contains only two distinct values not divisible by a given prime number $$p > 3$$, then $$\mathbf{O}^{p p^\prime p p^\prime}(G) = 1$$. This is done by using the classification of finite simple groups.

##### MSC:
 20C15 Ordinary representations and characters 20C33 Representations of finite groups of Lie type
##### Keywords:
character degrees; finite simple groups
CHEVIE
Full Text:
##### References:
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