THE WIDTH OF THE GROUP GL(6, K) WITH RESPECT TO A SET OF QUASIROOT ELEMENTS

摘要

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 E_6, but is also of independent interest. Bibliography: 41 titles.