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# A matrix-decomposition theorem for GLn (K)

Publikationstyp

Journal Article

Publikationsdatum

1999-09-01

Sprache

English

TORE-URI

Enthalten in

Volume

298

Issue

1-3

Start Page

39

End Page

50

Citation

Linear Algebra and Its Applications 1-3 (298): 39-50 (1999-09-01)

Publisher DOI

Scopus ID

Publisher

American Elsevier Publ.

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 x 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 PSLn(F3), n ∈ ℕ≥3, and PSL2n+1(F2), n ∈ ℕ. If G is such a group, then G has a conjugacy class Ω such that G = Ω2. In particular each element of G is a commutator.