Products of squares in finite simple groups

Liebeck, Martin; O’Brien, E.; Shalev, Aner; Tiep, Pham

doi:10.1090/S0002-9939-2011-10878-5

Products of squares in finite simple groups
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by Martin W. Liebeck, E. A. O’Brien, Aner Shalev and Pham Huu Tiep PDF

Proc. Amer. Math. Soc. 140 (2012), 21-33 Request permission

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.

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