Posting my weekly #VisualGroupTheory puzzle for #MathTwitter one day late this week. If you construct the left Cayley diagram of a group, and collapse the left cosets of a non-normal subgroup, then the result is not a group. This is shown on the left, for the subgroup. 1/3

Happy Friday, #MathTwitter. This week's #VisualGroupTheory puzzle involves groups I've posted about before. For each n>3, there are exactly 4 nonabelian groups of order 2^n that have an index-2 cyclic subgroup. 1/3

Happy Friday, #MathTwitter. For this week's #VisualGroupTheory puzzle, describe the following diagrams, in terms of groups acting on the quaternions Q_8. What are the groups and what do they represent? What is depicted by overlaying the first two diagram? Enjoy!

Good afternoon, #MathTwitter. I'm moving my weekly #VisualGroupTheory puzzles from Friday to Saturday. For this one, consider two squares, numbered 1 & 2, side-by-side, that are black or white. The "swap" operation transposes them, and the "toggle" operation flips. 1/3

This week's #VisualGroupTheory puzzle for #MathTwitter should be quite easy, but pleasing and insightful. Using only its subgroup lattice and the Sylow theorems, prove that A_5 is simple. The dashed circles indicate the conjugacy classes of the Sylow p-subgroups.

🚨🚨 #MathTwitter Announcement! 🚨🚨. As I'm going through and finalizing chapters in my #VisualAlgebra book, I'm recording a new set of YouTube videos in tandem. This will be more than twice as long as my existing #VisualGroupTheory playlist, with MUCH more content. 1/3 👇

This week's #VisualGroupTheory puzzle for #MathTwitter involves 3 unknown groups, whose Cayley diagrams are shown below. Determine which groups these are, and which two secretly decompose as a nontrivial direct product of two subgroups. The answer might surprise you!

Happy Friday, #MathTwitter, here's this week's #VisualGroupTheory puzzle. Three of these four are Cayley diagrams of the symmetric group S_4. The other is a different group. Figure out which one is not S_4, what group it is, and then label nodes (in all 4) with elements. Enjoy!

Happy Friday, #MathTwitter! Here is this week's #VisualGroupTheory puzzle. The group shown at the left is the Pauli group G_1 = <X,Y,X> on 1 qubit, where the generating matrices are shown below. It arises in quantum physics and computing. 1/3

Happy Friday! Time for another #VisualGroupTheory puzzle for #MathTwitter. A Cayley diagram is a way to visualize a group presentation. Here are 3 examples: the dihedral group D_4, the semi-dihedral group SD_8, and the alternating group A_4, where a=(123) and x=(12)(34). 1/2

Happy Friday, #MathTwitter! Time for the 4th installment of my weekly #VisualGroupTheory puzzle. For any n>3, there are exactly 4 non-abelian groups of order 2^n with an index-2 subgroup. Shown here for n=4 is the dihedral group D_n, the generalized quaternion group Q_16. 1/4

My professor is talking gibberish right now and I just CANT!!! #VisualGroupTheory.

Extra credit for wearing a costume to class Thursday. Any ideas? #Math412 #VisualGroupTheory.

Is it weird that I think this article on good mathematical writing is interesting? #noshame #VisualGroupTheory.