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Title: Examples for Groups
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Series: Algebra
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YouTube-Title: Algebra 5 | Examples for Groups
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Bright video: https://youtu.be/h0KVCg7RQCs
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Dark video: https://youtu.be/ksg9mPb3Ycc
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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: alg05_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: Do the rational numbers $\mathbb{Q}$ together with the multiplication form a group?
A1: No, because not all elements have inverses.
A2: No, because the identity element is missing.
A3: Yes, it’s a group.
A4: No, it’s not even a semigroup.
Q2: Consider a semigroup $(S, \circ)$ with two (different) elements $S = { e, a }$. Is it possible that we have $e = e \circ e$ and $a = a \circ a$?
A1: Yes, it’s possible.
A2: No, $a$ is not invertible.
A3: No, because we need to have a unique neutral element.
Q3: Consider a group $(S, \circ)$ with two (different) elements $S = { e, a }$, where $e$ is the neutral element. Is it possible that we have $e = e \circ e$ and $a = a \circ a$?
A1: Yes, it’s possible.
A2: No, because it would imply that $a$ is not invertible.
A3: No, because it would imply that we have two neutral elements.
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Last update: 2024-11
