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Let G = GL(2, R) and let K be a subgroup of R*. Prove that
Chapter 9, Problem 7E(choose chapter or problem)
QUESTION:
Let \(G=G L(2, \mathbf{R})\) and let K be a subgroup of \(\mathbf{R}^*\). Prove that \(H=\{A \in G \mid \operatorname{det} A \in K\}\) is a normal subgroup of G.
Questions & Answers
QUESTION:
Let \(G=G L(2, \mathbf{R})\) and let K be a subgroup of \(\mathbf{R}^*\). Prove that \(H=\{A \in G \mid \operatorname{det} A \in K\}\) is a normal subgroup of G.
ANSWER:Step 1 of 2
Let and let K be a subgroup of. To prove is a normal subgroup, defined as follows
Let, consider the group