### Abstract

The Ore conjecture, proved by the authors, states that every element of every finite non-abelian simple group is a commutator. In this paper we use similar methods to prove that every element of every finite simple group is a product of two squares. This can be viewed as a non-commutative analogue of Lagrange's four squares theorem. Results for higher powers are also obtained.

Original language | English (US) |
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Pages (from-to) | 21-33 |

Number of pages | 13 |

Journal | Proceedings of the American Mathematical Society |

Volume | 140 |

Issue number | 1 |

DOIs | |

State | Published - 2012 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Liebeck, M. W., O'brien, E. A., Shalev, A., & Tiep, P. H. (2012). Products of squares in finite simple groups.

*Proceedings of the American Mathematical Society*,*140*(1), 21-33. https://doi.org/10.1090/S0002-9939-2011-10878-5