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Title: Conjugate Subgroups
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Series: Algebra
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Chapter: Groups
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YouTube-Title: Algebra 13 | Conjugate Subgroups
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Quiz: Test your knowledge
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Subtitle on GitHub: alg13_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $(G, \circ)$ be a group and $\varphi: G \rightarrow G$ be a group automorphism. What is not correct?
A1: $\varphi$ is bijective.
A2: $\varphi$ is a group homomorphism.
A3: $\varphi^{-1}$ exists and is a group homomorphism.
A4: $\varphi[G] \neq G$
Q2: Let $(G, \circ)$ be a group and $\varphi: G \rightarrow G$ be an inner automorphism. What is not always correct?
A1: There is $g \in G$ such that $\varphi(x) = g x g^{-1}$ for all $x \in G$.
A2: There is $g \in G$ such that $\varphi^{-1} (x) = g^{-1} x g$ for all $x \in G$.
A3: $\varphi$ is bijective.
A4: There is a $g \in G$ such that $\varphi(x) = g$ for all $x \in G$.
Q3: Let $(G, \circ)$ be a group and $U,V \subseteq G$ conjugate groups. What is always correct?
A1: $U = V$.
A2: $U = G$.
A3: There is an element $g \in G$ such that $g U = g V$.
A4: There is an inner automorphism $\varphi$ such that $\varphi[U] = V$.
Q4: Let $(G, \circ)$ be an abelian group and $U,V \subseteq G$ conjugate groups. What is not always correct?
A1: $U = V$.
A2: $U = G$.
A3: There is an element $g \in G$ such that $g U = g V$.
A4: There is an inner automorphism $\varphi$ such that $\varphi[U] = V$.
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Date of video: 2024-11-05
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Last update: 2025-11
