Abstract Algebra - 2.3 Elementary Properties of a Group

We look closely at a few of the properties of groups and their proofs, including cancellation, uniqueness of inverses and identities and the socks-shoes property. We will utilize the WTS, Given, Proof format for our proofs. We will also compare the multiplicative and additive notations and how to translate them and how to use the known properties of exponents to rewrite an expression using positive exponents.

Video Chapters:
Intro 0:00
Cancellation Property 0:26
Uniqueness of Identity 6:35
Uniqueness of Inverses 9:58
Socks-Shoes Property 11:44
Multiplicative vs Additive Group Notation 14:00
Rewrite Using Positive Exponents 16:47
Up Next 19:15

This playlist follows Gallian text, Contemporary Abstract Algebra, 9e.

[christopherwilliams]

Thanks for this series! It's actually helping me with my 500-level abstract algebra course in grad school. One question though: In the section on uniqueness of identities, did you really mean to write "Let e and e' be inverses?" Wouldn't we want to say, "Let e and e' be identities?"

[jujubee]

17:06 would it be fair to do it this way as well?:
(going to use asterik (*) to denote operation)
using identity property, e*(a^-2)*e*(b^-4) = (a^-2) * (b^-4), using substitution, (a^5)*(a^-2)*(b^7)*(b^-4) and then adding the exponents would yield a^3 * b^3