Implementation of the Todd-Coxeter Algorithm to Finitely Presented Groups

Sammanfattning: This work presents the notion of free groups and the definition of a group using generators and relations. We use the Todd-Coxeter Algorithm in order to solve the coset enumeration problem for the finitely presented groups: $D_4,\, A_4,\, A_5,\, S_3,\, S_4,\, S_5,\, PSL_2(7),\, PSL_2(9)$. Then we use these presentations in order to prove the exceptional isomorphisms $A_5\cong PSL_2(5) \cong SL_2(4)$, $PSL_2(9)\cong A_6$ and $SL_3(2)\cong PSL_2(7)$.