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Title: Abelian Groups
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Series: Algebra
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Chapter: Groups
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YouTube-Title: Algebra 7 | Abelian Groups
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Original video for YT-Members (bright): Watch on YouTube
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Original video for YT-Members (dark): 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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Subtitle on GitHub: alg07_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
00:00 Intro
00:40 Symmetries of a triangle as a group
00:40 Symmetries of a triangle as a group
03:39 Symmetry group as set of permutations
06:05 Example of non-commutativity
07:49 Definition: abelian groups
07:49 Examples: numbers form abelian groups
09:25 Group of order 3 is abelian
13:00 Correction: The second case can actually not happen for a group with only 3 elements.
13:26 How many elements are needed to be non-abelian?
14:55 Credits
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Subtitle in English (n/a)
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Quiz Content
Q1: Which of the following semigroups is not abelian?
A1: $\mathbb{Z}$ together with addition.
A2: $\mathbb{C}$ together with multiplication.
A3: $\mathbb{C}^{2 \times 2}$ together with matrix addition.
A4: $\mathbb{R}^{2 \times 2}$ together with matrix multiplication.
Q2: Which of the symmetric groups $S_n$ is not abelian?
A1: $S_1$
A2: $S_2$
A3: $S_3$
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Last update: 2025-11
