Math Problem Statement
Let G = GL(2, R) and let K be a subgroup of R∗. Prove that H = {A ∈ G | det(A) ∈ K} is a normal subgroup of G.
Solution
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Math Problem Analysis
Mathematical Concepts
Group Theory
Linear Algebra
Subgroups
Determinants
Normal Subgroups
Formulas
det(AB) = det(A) * det(B)
det(A^-1) = 1/det(A)
det(ghg^-1) = det(g) * det(h) * det(g^-1)
Theorems
Subgroup Criteria
Normal Subgroup Definition
Closure Properties of Subgroups
Suitable Grade Level
Graduate