### A Somewhat Productive Weekend

I had a fairly productive weekend. I got two stacks of tests graded.

I also fixed my mailbox. The door had fallen off and I screwed it back on. I don't know if I did it right and it might fall off again. I am not the handiest person in the world. But I'll never learn if I don't try.

I also solved a problem in group theory that has been bedeviling me for some time now. I wanted to find a permutation group that was isomorphic to the multiplicative matrix group of 2x2 matrices over the finite field of size 3 (or GF(3)). There is a simple algorithm that will map a group with n elements to a subset of the symmetric group Sym({1..n}). (That's an ugly way to describe the group, but I have no choice because subscripting seems to have disappeared from livejournal's rich text editor. Bah!). Anyway, n in this case is equal to 24, and I wanted a smaller n.

Anyway, I discovered that the permutation group generated by the permutations (1 2 3 4 5 6)(7 8) and (1 5 7 4 2 8)(3 6) is isomorphic to the 2X2 matrix group over GF(3). Yay!!

I also fixed my mailbox. The door had fallen off and I screwed it back on. I don't know if I did it right and it might fall off again. I am not the handiest person in the world. But I'll never learn if I don't try.

I also solved a problem in group theory that has been bedeviling me for some time now. I wanted to find a permutation group that was isomorphic to the multiplicative matrix group of 2x2 matrices over the finite field of size 3 (or GF(3)). There is a simple algorithm that will map a group with n elements to a subset of the symmetric group Sym({1..n}). (That's an ugly way to describe the group, but I have no choice because subscripting seems to have disappeared from livejournal's rich text editor. Bah!). Anyway, n in this case is equal to 24, and I wanted a smaller n.

Anyway, I discovered that the permutation group generated by the permutations (1 2 3 4 5 6)(7 8) and (1 5 7 4 2 8)(3 6) is isomorphic to the 2X2 matrix group over GF(3). Yay!!

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