Homework Statement
1. Let n ≥ 2. Let H = {σ ∈ S_n: ord(σ) = 2}. Decide whether or not H is a subgroup of S_n.
2. Let G be a group of even order. Show that the cardinality of the set of elements of G that have order 2 is odd.
The Attempt at a Solution
1. I have no idea where to start with...
Let α (alpha) all in S_n be a cycle of length l. Prove that if α = τ_1 · · · τ_s, where τ_i are transpositions, then s geq l − 1.
I'm trying to get a better understanding of how to begin proofs. I'm always a little lost when trying to solve them.
I know that I want to somehow show that s is...
Homework Statement
Let α (alpha) all in S_n be a cycle of length l. Prove that if α = τ_1 · · · τ_s, where τ_i are transpositions, then s geq l − 1.Homework Equations
The Attempt at a Solution
What I was actually looking for is where to start with this proof. I don't want the answer, just a...