need help 37·Let D" be the dihedral group of order 2n. Docribe its embedding in Ss ao deter. mined by Cayley's theorem. (Note: The embedding will depend on your chicoe of an ordering of t...
I help help with 34-40
33. I H is a subgroup of G and g G, prove that gHg-1 is a subgroup of G. Also, prove that the intersection of gH for all g is a normal subgroup of G. 34. Prove that 123)(min-1n-)1) 35. Prove that (12) and (123 m) generate S 36. Prove Cayley's theorem, which is the followving: Any finite group is isomorphic to a subgroup of some S 37. Let Dn be the dihedral group of...
Problem 3.[10 points.] Let D. be the dihedral group of order 2n. Let H = (r) be the subgroup of D, consisting of all rotations. Prove that every subgroup of H is normal in D Solution: