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