Readthrough of Abstract Algebra, Theory and Applications - Part 11 : Homomorphisms
A reading (complete for all the exposition though not going through all exercises for the sake of time) of the August 2021 version of Tom Judson's Abstract Algebra: Theory and Applications (link to it is http://abstract.ups.edu/, where the pdf is freely hosted by its authors), done on Twitch at / xdd4less3 .
Resources used for streaming are OBS, and the workings out are done on MS Paint.
CHAPTERS :
0:00:00--0:38:00 : Homormorphisms (Reading)
0:38:00-0:39:45 : Intermission
0:39:45-2:17:52 : Homomorphisms (Problems)
If you're still reading this description.. well, have a wonderful day, and take it as easy as you can! Oh, and make sure to stay hydrated -
NOTE : There is a fairly large technical error in the problems section - I claim that Aut(S_{n}) is isomorphic to S_(n(n-1)/2) - this is incorrect. I had used that logic that since S_{n} is generated by (n-1) transpositions, then the permutation group of this describes the automorphism group. This is in the right direction, but is not exactly the case - since, if there are two permutations (a, b) and (c, b), we have (a, b)(c, b)(a, b) = (a, c) generated - in a sense, we need to search for a "minimum" set of generators of S_{n} (which (a, b), (c, b), and (a, c) are not). I'll leave the rest of the details to the interested reader and the article https://en.wikipedia.org/wiki/Automor... on this topic.
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