-
Title: Klein Four-Group
-
Series: Algebra
-
YouTube-Title: Algebra 11 | Klein Four-Group
-
Bright video: https://youtu.be/YakBqCwtBTU
-
Dark video: https://youtu.be/e5Q8VGC4Zwc
-
Ad-free video: Watch Vimeo video
-
Quiz: Test your knowledge
-
Dark-PDF: Download PDF version of the dark video
-
Print-PDF: Download printable PDF version
-
Thumbnail (bright): Download PNG
-
Thumbnail (dark): Download PNG
-
Subtitle on GitHub: alg11_sub_eng.srt missing
-
Timestamps (n/a)
-
Subtitle in English (n/a)
-
Quiz Content
Q1: Let $(G, \circ)$ be a group and $H \subseteq G$ be a subset. What does $H \leq G$ mean?
A1: $H$ together with the binary operation $\circ$ forms a group.
A2: $H$ is empty.
A3: The neutral element of $(G, \circ)$ is not an element of $H$.
A4: $H$ is biggest subgroup of $G$.
Q2: Let $(G, \circ)$ be a group and $H \subseteq G$ be a non-empty subset. What is equivalent to $H \leq G$?
A1: $a \circ b \in H$ and $a^{-1} \in H$ for every $a,b \in H$.
A2: $a \circ b \in H$ and $a \in H$ for every $a,b \in H$.
A3: $a \circ b \in H$ and $a^{-1} \in H$ for every $a,b \in G$.
A4: $a \circ b^{-1} \in H$ for every $a,b \in G$.
Q3: Let $(G, \circ)$ be a group with four elements. What is always correct?
A1: $G$ is an abelian group.
A2: $G$ is the Klein four group.
A3: $G$ is $\mathbb{Z}/4\mathbb{Z}$
A4: $G$ has 3 subgroups.
-
Last update: 2024-11
