# Abstract Algebra.

by m-chan
Tags: abelian, algebra, disjoint cycles, group, permutations
 P: 2 I have 2 algebra questions which are stumping me, I just can't seem to use my notes to figure them out! 1. Let α, β ∈ S17 where α = (17 2)(1 2 15 17 ), β = (2 3 16)(6 16 17 ). Determine η, as a product of disjoint cycles, where αη = β. 2. Let G be a group in which a^2 = 1 for all a ∈ G. Prove that G is Abelian. Hint: Consider (ab)^2. HELP PLEASE :(
 Mentor P: 20,436 For 2, consider what (ab)2 equals.
 P: 2 Right, I've figured out 2, thanks Mark44 and I've done some of 1, but I'm stuck at the end of the question. I have η= (2 17)(17 15 2 1)(2 3 16)(6 16 17), but I'm not sure if that's right though. I also don't know where to go from there.

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