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 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics