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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
Software:
CHEVIE
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