We call an element of the finite general linear group GL(V) fat if it leaves invariant and acts irreducibly on a subspace of dimension greater than dim(V)/2. Fat elements can be identified efficiently in practice and are intended to provide the basis for new algorithms dealing with linear groups. We first develop a framework necessary to study fat elements obtaining new results in elementary number theory, theory of finite fields (counting certain irreducible polynomials) and group theory (regarding irreducible semilinear mappings). Then, guided by Aschbacher's theorem, we investigate the occurrence of fat elements in various maximal subgroups of GL(V).
|Qualification||Doctor of Philosophy|
|Award date||21 Jan 2019|
|Publication status||Unpublished - 2019|