A matrix-decomposition theorem for GLn(K)

✍ Scribed by Florian Bünger; Klaus Nielsen

• Book ID: 104156701
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 101 KB
• Volume: 298
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00138-x

✦ Synopsis

Given an arbitrary commutative field K, n ∈ N 3 and two monic polynomials q and r over K of degree n -1 and n such that q(0) = 0 = r(0). We prove that any non-scalar invertible n × n matrix M can be written as a product of two matrices A and B, where the minimum polynomial of A is divisible by q and B is cyclic with minimum polynomial r. This result yields that the Thompson conjecture is true for PSL n (F 3 ), n ∈ N 3 , and PSL 2n+1 (F 2 ), n ∈ N. If G is such a group, then G has a conjugacy class such that G = 2 . In particular each element of G is a commutator.