Recent content by JojoF

Homework Statement Let ##G## be a group of order ##2p## with p a prime and odd number. a) We suppose ##G## as abelian. Show that ##G \simeq \mathbb{Z}/2p\mathbb{Z}## Homework EquationsThe Attempt at a Solution Intuitively I see why but I would like some suggestion of what trajectory I could...

What if I write Dn = {e,r,r2,..., rn-1,a,ar,ar2,..., arn-1} = <a,r | a2, rn, (ar)2 > a set b = ra ⇒ r = ba-1 = ba and we can therefore rewrite Dn = {e, ba, (ba)2, ... , (ba)n-1, a(ba), ..., a(ba)n-1 } = < a,b | a2, b2, (ab)n>

Of course you are right. I just copied an exercise verbatim. So let me restate the question. Let n ≥ 2 Show that the dihedral group Dn is equal to <a,r | a2, rn, (ab)2> where the dihedral group is the group of symetries of a regular n-gon

Homework Statement let n ≥ 2 Show that Dn = < a,b | a2, b2, (ab)n> Homework EquationsThe Attempt at a Solution I see that a and b are involutions and therefore are two different reflections of Dn. If we set set b = ar where r is a rotation of 2π/n And Dn = <a,r | a2, rn, (ab)2 > I am unsure...