Characterizations of the solvable radical
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Colleges, School and Institutes
We prove that there exists a constant k with the property: if C is a conjugacy class of a finite group G such that every k elements of C generate a solvable subgroup, then C generates a solvable subgroup. In particular, using the Classification of Finite Simple Groups, we show that we can take k = 4. We also present proofs that do not use the Classification Theorem. The most direct proof gives a value of k = 10. By lengthening one of our arguments slightly, we obtain a value of k = 7.
|Number of pages||10|
|Journal||Proceedings of the American Mathematical Society|
|Publication status||Published - 1 Apr 2010|
- Solvable radical, generation by conjugates