Abstract Algebra, Lec 9A: U(n) Group Cayley Table on Mathematica, Proof of Theorem on Cyclic Groups скачать в хорошем качестве

Abstract Algebra, Lec 9A: U(n) Group Cayley Table on Mathematica, Proof of Theorem on Cyclic Groups

"Contemporary Abstract Algebra", by Joe Gallian: https://amzn.to/2ZqLc1J Check out my blog at: https://infinityisreallybig.com/ Abstract Algebra Playlist:    • Abstract Algebra Course, Lecture 1: Introd...   (0:00) Reminder about Exam 1. (1:00) Lecture overview. (1:34) Mathematica Code to Make Cayley Tables for U(n), the group of units under multiplication modulo n. (5:46) Criterion for a^i = a^j (both when "a" has infinite order and finite order. (7:38) Proof of the criterion when the order |a| = infinity. (12:11) Proof of the criterion (set equality portion) when the order |a| = n (note r should be less than n in proof). (20:10) Proof of the criterion for a^i = a^j when the order |a| = n. (25:54) Corollaries of condition for when a^i = a^j. (30:42) Orders of (and subgroups generated by) powers of generators of finite cyclic groups. (31:44) Lemma: Suppose G is a group, H is a subgroup of G, and "a" is an element of G. If a is an element of H, then the cyclic subgroup of G generated by "a" is a subgroup of H (and its proof). AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.