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Elements in finite classical groups whose powers have large 1-Eigenspaces

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.
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Alice C. Niemeyer, Cheryl E Praeger. Elements in finite classical groups whose powers have large 1-Eigenspaces. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 1 (1), pp.303--312. ⟨10.46298/dmtcs.3908⟩. ⟨hal-01179225⟩

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