### 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) |
---|---|

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 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*140*(1), 21-33. https://doi.org/10.1090/S0002-9939-2011-10878-5

**Products of squares in finite simple groups.** / Liebeck, Martin W.; O'brien, E. A.; Shalev, Aner; Tiep, Pham Huu.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 140, no. 1, pp. 21-33. https://doi.org/10.1090/S0002-9939-2011-10878-5

}

TY - JOUR

T1 - Products of squares in finite simple groups

AU - Liebeck, Martin W.

AU - O'brien, E. A.

AU - Shalev, Aner

AU - Tiep, Pham Huu

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=82055165373&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=82055165373&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2011-10878-5

DO - 10.1090/S0002-9939-2011-10878-5

M3 - Article

VL - 140

SP - 21

EP - 33

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -