1.6.8 Fields, Groups, Rings

Problem: For a given group \( G \) and its subgroup \( H \) : a) describe (left) cosets, b) find out if the factor group is defined, c) if the factor group is defined, give an example of an isomorphic group. \[ G=(G L(n, \mathbb{R}) \cdot \cdot), H=\{A \in G L(n \cdot \mathbb{R}):|\operatorname{det} A|=1\} . \]