[old series] Abstract Algebra Lecture 12 Part 1

Twelfth lecture in abstract algebra. Topics include commutativity versus anticommutativity, an introduction to finite groups, Cayley tables, and the quaternion group. This lecture is in four parts.

[Obito]

Thank you for your videos! I really enjoy them :)

[oncexist]

Hello, sir

At about 16:45, when trying to show <C, *> is a quasigroup where * is defined as z1 * z2 = z1 times conjugate(z2), do z1, z2 have solutions if z1 or z2 are (0, 0)

since if regular multiplication in complex numbers is (a, b)(c, d) = (ac - bd, ad + bc), and in this example we can translate this multiplication to (a, b) * (c, d) = (a, b)(c, -d) = (ac + bd, -ad + bc) = (0c + 0d, -0d + 0c) = (0, 0) if (a, b) = 0, whatever (c, d) may be, and similarly, (a, b) * (0, 0) = (a0 + b0, -a0 + b0) = (0, 0) if (c, d) = (0, 0) whatever (a, b) may be.