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Title: Cyclic Groups
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Series: Algebra
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Chapter: Groups
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YouTube-Title: Algebra 14 | Cyclic Groups
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Bright video: Watch on YouTube
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: alg14_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark 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 $S \subseteq G$ a subset. What is correct?
A1: $\langle S \rangle$ is the smallest subgroup $U$ with the property $S \subseteq U$.
A2: $\langle S \rangle$ is the largest subgroup $U$ with the property $S \subseteq U$.
A3: $\langle S \rangle$ is the largest subgroup $U$ with the property $U \subseteq G$.
A4: $\langle S \rangle$ is the smallest subgroup $U$ with the property $U \subseteq S$.
Q2: Let $(G, \circ)$ be a group. What is always correct?
A1: $\langle \emptyset \rangle = {e }$
A2: $\langle \emptyset \rangle = G$
A3: $\langle \emptyset \rangle = \emptyset $
A4: $\langle \emptyset \rangle = G \setminus { e }$
Q3: Let $(\mathbb{Z}, +)$ be the group given by the integers with the addition. What is not correct?
A1: $\mathbb{Z} = \langle 0\rangle$
A2: $\mathbb{Z} = \langle 1 \rangle$
A3: $\mathbb{Z} = \langle 0 , 1 \rangle$
A4: $\mathbb{Z} = \langle -1, 0 , 1 \rangle$
A5: $\mathbb{Z} = \langle \mathbb{Z} \rangle$
A6: $\mathbb{Z}$ is a cyclic group.
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Date of video: 2024-11-06
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Last update: 2025-11
