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Title: Groups
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Series: Algebra
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YouTube-Title: Algebra 4 | Groups
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Bright video: https://youtu.be/VXkJybS-LAs
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Dark video: https://youtu.be/CrkBtG2JyfI
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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: alg04_sub_eng.srt missing
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Timestamps
00:00 Introduction
00:55 Semigroup with inverses
01:42 First definition of a group
03:16 Second definition of a group
05:00 Proof for equivalence of definitions
10:10 Credits
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Subtitle in English (n/a)
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Quiz Content
Q1: Consider the natural numbers ${0, 1, 2, \ldots}$ together with the addition. Do they form a group?
A1: No, because the inverses are missing.
A2: No, because the identity element is missing.
A3: Yes, it’s a group.
A4: No, it’s not even a semigroup.
Q2: Consider the integers ${\ldots, -1, 0, 1, 2, \ldots}$ together with the addition. Do they form a group?
A1: No, because the inverses are missing.
A2: No, because the identity element is missing.
A3: Yes, it’s a group.
A4: No, it’s not even a semigroup.
Q3: Let $(S, \circ)$ be group with identity $e$. What is always correct?
A1: $e^{-1} = e$
A2: $a \circ b = b \circ a$ for all $a,b \in S$.
A3: $a \circ e = e $ for all $a \in S$.
A4: $a^{-1} \circ a = a$ for all $a \in S$.
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Last update: 2024-11
