Abstract Algebra: practice problems, chapter 2 and 3 Gallian, 9-1-16

[kynnjones]

Wow! Prof. Cook: you pulled off that matrix counterexample on the whiteboard! Respect!

[cubuffs]

i just want to commend your humble and Christ-like teaching style!

[xoppa]

25:10 there must be more elements in U(91), which are relatively prime to 91, for example 2, 3, etc.

[thomasuga]

This shit is beyond me I’m struggling in calculus...

[xoppa]

5:13 to show that b^-1 a^-1 is the inverse of (ab), do you have to multiply (ab) by b^-1 a^-1 on the left as well?
In other words is it sufficient to check (ab)(b^-1 a^-1) = e
and not have to check that
(b^-1 a^-1)(ab) = e

[jonkeuviuhc]

if (ab)^(-2) =b^(-2) a^(-2) then b^(-1)a ^(-1) b^(-1) a^(-1) = b^(-2) a^(-2). Then you multiply left with a and right with b and you get b ^(-1) a^(-1) = a^(-1) b^(-1) for any a^(-1) and b^(-1) in the group, therefore the group is abelian.

Edit: I though this is the proof for the second problem, but I see this is the solution to the 3rd problem.

[hussainalasmawi]

Dr.Cook the questions that in Gallian is much more difficult than what in the lecture so is it enough for the student to understand the questions that you put in the website and in the lectures?

[justfunu]

anyone have solutions of chpter 2 and chpter3 of book algebra by gallian

[jacksonadams]

Too bad this has no real life applications