How to Visualize Subgroups

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[ramaronin]

i was completely waiting for Lagrange groups to show up and only at the end you tease about it. Please, make a video about it

[dicipuluscaptiosus]

so far this channel is a tribute to pure mathematics, this is really going to be great
this videos have the same effect of cartoons, maybe is the colors and the animations, but it feels stimulating.

[shaneri]

Visual Group Theory <3

thank you Luca and Sophia!

[OpPhilo]

Thank you sir❤ and mam❤. Please next part. I am curious about to knowing deeply.

[paulfoss]

My favorite cayley diagrams to draw are the one's for A4, S4 and A5. The diagrams almost feel like they're drawing themselves. My least favorite (of the diagrams that are in any way reasonable to draw) is Q8 because it has two order four generators which tangle up on the page. Maybe building a 3D diagram would make more sense.

And the most illuminating Caley Diagram to draw for me I think was the Frobenius 21 group, I was curious when I saw it was the smallest non-Abelian group of odd order, and I wanted to know why that was, and after drawing it out I was able to see how the order 3 generator performed an automorphism on the 7 cycle, and that made semidirect products a lot more intuitive. Dihedral groups work the same way, but sometimes you need to add a little complexity to see why invoking heavier machinery like automorphisms is useful, and F21 strikes a good balance.

And with a better understanding of semidirect products, I was able to see more clearly how V4 is normal in A4. Though I didn't really get it until a made a modular origami tetrahedron with all three pairs of opposite edges given their own color. I could see that there were four actions that left the colors unchanged, and rotating about any vertex rotated the colors on every vertex.

[ijkhugeplay]

Thanks for video. Always wanted to understand groups naturally

[samueldeandrade]

1:15 This is just false. Mathematicians definitely flip and rotate geometrical objects. Or vectorial or symbolic representations.

[ramaronin]

tã tã tãããã tã tã tããã !!!! vai 🇧🇷 🇧🇷 🇧🇷 é teeetra é teeetra

[ValidatingUsername]

If you don’t want a mathematical node for the visualization ven diagrams are the most appropriate for subgroups

[rudraksh]

Can you explain graph theory of computer science in complete detail please

[janurek]

7:55 Shouldn’t it suppose to be <2> < C6?

[Mahi-ki]

i want to learn about general relativity. But i have lack knowledge about reinmen curvature, ricci curvature, geodesics and cristofal symbol. Can you give videoes about this topic. Please

[willnewman]

I do not know why you are calling cyclic subgroups "orbits." These are not the usual orbits one sees in group theory.