The structure of GL(6,K) with respect to a certain family of conjugacy classes the elements of which are said to be quasiroot is studied. Namely, it is proved that any element of GL(6,K) is a product of three quasiroot elements, and a complete description of the elements that are products of two quasiroot elements is given. The result arises in studying the width of the exceptional groups of type E6, but is also of independent interest.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 423, 2014, pp. 183–204.
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Pevzner, I.M. The Width of the Group GL(6,K) with Respect to a Set of Quasiroot Elements. J Math Sci 209, 600–613 (2015). https://doi.org/10.1007/s10958-015-2516-0
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DOI: https://doi.org/10.1007/s10958-015-2516-0