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Title: Subgroups under Homomorphisms
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Series: Algebra
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YouTube-Title: Algebra 12 | Subgroups under Homomorphisms
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Bright video: https://youtu.be/UaS_JcGJT3I
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Dark video: https://youtu.be/cf_EFqO3OKk
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Ad-free video: Watch Vimeo video
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: alg12_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $(G, \circ)$, $(H, \ast)$ be two groups, $\varphi: G \rightarrow H$ a group homomorphism, and $a \in H$. Is $\varphi^{-1}[{ a }]$ a subgroup of $G$.
A1: No, it’s a subgroup of $H$.
A2: Yes, it’s proven in the video.
A3: It’s only a subgroup if $a$ is the neutral element of $H$.
A4: No, it’s never a subgroup.
Q2: Let $(G, \circ)$, $(H, \ast)$ be two groups and $\varphi: G \rightarrow H$ be a group homomorphism. What is always a subgroup of $H$?
A1: $\mathrm{Ker}(\varphi)$
A2: $\varphi^{-1}({ e_H })$
A3: $\mathrm{Ran}(\varphi)$
A4: ${e_G }$
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Last update: 2024-11
