T-systems of the Mathieu group M(11)

Let M11 denote the Mathieu group of order 7,920, and let Fn denote the free group of rank n, where n ≥ 3. Suppose that R and S are normal subgroups of Fn such that Fn/R≅ Fn/S≅ M11. The main result of this dissertation asserts that there exists an automorphism theta of Fn such that Rtheta = S. In other words, M11 has a unique Tn-system for each n ≥ 3.