Abstract
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.
Original language | English |
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Pages (from-to) | 1161-1170 |
Number of pages | 10 |
Journal | Proceedings of the American Mathematical Society |
Volume | 138 |
Issue number | 04 |
DOIs | |
Publication status | Published - 1 Apr 2010 |
Keywords
- Solvable radical
- generation by conjugates