# Characterizations of the solvable radical

Research output: Contribution to journal › Article

## Authors

## Colleges, School and Institutes

## 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.

## Details

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 |

Publication status | Published - 1 Apr 2010 |

## Keywords

- Solvable radical, generation by conjugates