UC Irvine

In this dissertation, we compute the essential p-dimension of the split finite quasi-simple groups of classical Lie type at the defining prime, specifically the quasi-simple groups arising from the general linear and special linear groups, the symplectic groups, and the orthogonal groups. Also, for odd primes l not equal to the defining prime, we compute the essential l-dimension of the finite groups of classical Lie type, specifically the general linear and special linear groups, the symplectic groups, the orthogonal groups, and the unitary groups, and the non-abelian simple factors in their Jordan-Hölder series.