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Title: Integers Modulo m ⤳ Abelian Group
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Series: Algebra
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YouTube-Title: Algebra 8 | Integers Modulo m ⤳ Abelian Group
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Bright video: https://youtu.be/s6dUlR3TrgI
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Dark video: https://youtu.be/4IS-VVlzwBM
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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: alg08_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: Given a natural number $m \in \mathbb{N}$, is it possible to find an abelian group of order $m$?
A1: Yes, we can take the group $\mathbb{Z}/m \mathbb{Z}$.
A2: No, but for prime numbers $m$ we can take the group $\mathbb{Z}/m \mathbb{Z}$.
A3: No, we $m = 5$ there is no abelian group.
A4: Yes, we can take the symmetric group $S_m$.
Q2: Which of the following statements is not correct?
A1: $7 = 1 \mod 2$
A2: $7 = 7 \mod 8$
A3: $7 = 3 \mod 2$
A4: $17 = 10 \mod 7$
A5: $20 = 10 \mod 11$
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Last update: 2024-11
