Abstract
In [4], Gorenstein provided a short argument that a minimal counterexample to Thompson’s N-Group Theorem must be either “quasi-thin” or “of uniqueness type.” In this note, we offer an even shorter proof that a minimal counterexample to the Odd Order Theorem of Walter Feit and John G. Thompson must have a “strongly p-embedded subgroup”. Only the brevity of the proof may be surprising. Certainly the thrust of Chapter 4 of the Odd Order Paper [l] is to produce far sharper uniqueness statements and it has long been clear that the difficulty of the Odd Order Problem resides in the fact that strongly p-embedded subgroups are far more intractable for odd primes p than for p = 2. However, in case this point has been missed by some and in the hope that someone will have a truly new and wonderful idea to treat strongly p-embedded subgroups, we offer the following result.
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