Elements in finite classical groups whose powers have large 1-Eigenspaces
Alice Niemeyer (1) (2), Cheryl Praeger (1) (3)
(1) School of Mathematics and Statistics [Crawley, Perth]
(2) Lehrsthul D für Mathematik [Aachen]
(3) King Abdulazziz University
Abstract
We estimate the proportion of several classes of elements in finite classical groups which are readily recognised algorithmically, and for which some power has a large fixed point subspace and acts irreducibly on a complement of it. The estimates are used in complexity analyses of new recognition algorithms for finite classical groups in arbitrary characteristic.
