On Products of Involutions
In 1974, A. Sampson  gave a rather technical matrix-theoretic proof that any complex matrix of determinant ±1 can be written as a product of finitely many involutions. A brash, young (at the time) algebraist, I quickly saw a group-theoretic proof that gives the same result for matrices over any field, and involves very little computation. Indeed, my proof occupied one and a half typed pages, most of it devoted to a couple of special cases. I sent a copy off to Hans Schneider for publication in Linear Algebra and its Applications, and distributed copies in the mailboxes of a few selected colleagues. One of those colleagues was Paul Halmos (that was a different time and place for both of us). A few hours later, Paul passed me in the hall.
KeywordsNormal Subgroup Simple Group Companion Matrix Finite Order Companion Matrice
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