Recent content by TDA120

\langleRight. I wasn’t thinking the right way; thanks!\rangle

Hi I like Serena!, Thanks again! Yes I three-double checked with all sorts of commutators. Is this enough proof for ρkσ = σρ-k ρkσ *ρkσ = id as ρkσ is a reflection Then ρkσ *ρk = σ And ρkσ = σρ-k If n is even, Dn /[Dn,Dn] consists of four elements, id and three others: ρ, σ and...

Thanks! I think this meant I could make some new steps.!? ρkρlσρ-k(ρlσ)-1= ρkρlσρ-kσρ-l= ρk+lσσρk-l= ρ2k So, every commutator will be either id or ρ2k As 2k is a multiple of ρ2, [Dn,Dn] is generated by ρ2. So [Dn,Dn] = \left\langle ρ2k \right\rangle = {id, ρ2, ρ4, …, ρn-2} if n is even and...

1. Homework Statement My challenge is as follows: Let Dn be the dihedral group (symmetries of the regular n-polygon) of order 2n and let ρ be a rotation of Dn with order n. (a) Proof that the commutator subgroup [Dn,Dn] is generated by ρ2. (b) Deduce that the abelian made Dn,ab is...

Homework Statement Let n be a whole number of the form ##n=x^2+1## with ##x \in Z##, and p an odd prime that divides n. Proof: ##p \equiv 1 \mod 4##.Homework Equations The Attempt at a Solution The only relevant case is if p=3 mod 4. If I try to calculate mod 3, or mod 4, or mod p, I'm not...