Visualizing Group Theory 1
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users point people to it as a go-to visual introduction when asked how to picture groups, Cayley graphs and products like semidirect products.
Recommended by 4 people across 4 different months, 2013 to 2017.
What it is
The first video in Nathan Carter's Visual Group Theory series, a short introduction to what groups are, shown through Cayley-graph style diagrams and symmetries. It is presented as a clear visual walkthrough of basic group structure.
What people said
Recommends Stahl · 2013-04 · Mathematics Stack Exchange · on “Can $C_{10}$ be isomorphic to $C_5\times C_2$?”
You might find this [this video] useful for your strategy of visualizing groups as graphs. The relevant mathematics starts at about 2:00.
Recommends quapka · 2015-05 · Mathematics Stack Exchange · on “Textbooks for visual learners”
@Rzeta although you might not be interested in Topology and Algebra and you specifically asked for books, I will still link you to few videos. Maybe it will interest you in the future: Tadashi Tokieda's Topology/Geometry lectures [LINK] and Nathan Carter's Visual Group Theory - video [this video] and also as a book [LINK] .
Recommends Santana Afton · 2017-02 · Mathematics Stack Exchange · on “"Semidirect product" of graphs?”
If you haven't already, I would suggest that you watch this short video by Nathan Carter about how to visualize the semidirect product. It might give you some inspiration on how to achieve this for general graphs, instead of Cayley graphs. [this video]
Recommends MathematicianByMistake · 2017-10 · Mathematics Stack Exchange · on “How can I visualise groups in Group Theory?”
The video " Visualizing Group Theory 1 [this video] " is in my opinion an almost ideal visualization-and a good introductory summary-of groups. Also, reading the classic book " Symmetry" [LINK] by Herman Weyl is a must.
Cites Omar Shehab · 2016-11 · Mathematics Stack Exchange · on “Visualizing $S_3 \rtimes D_4$”
I am trying to visualizing $S_3 \rtimes D_4$ following this video [this video] . Here, $S_3$ is the symmetric group over three symbols and $D_4$ is the dihedral group of order $8$. The semidirect product is defined as follows as per the definition given here [LINK] . Outer semidirect product: Let $G$ be $G = S_3 \rtimes_\varphi D_4$, $S_3 \triangleleft G$, and $D_4 < G$. Let $Aut(S_3)$ denote the group of all automorphism of $S_3$. The map $\varphi : D_4 \to Aut(S_3)$ defined by $\varphi (h) = \varphi_h$, conjugation by $h$, where $\varphi (h) (n) = \varphi_h (n) = h n h^{-1}$ for all $h$ in $D_4$ and all $n$ in $S_3$, is a group homomorphism. Together $S_3$, $D_4$, and $\varphi$ determine $G$ up