Dihedral Groups - Semi-direct Products - Part 2

The symmetry group of a regular n-gon (the dihedral group of order 2n) is an internal semi-direct product of its index 2 subgroup of rotations and any order 2 subgroup generated by a single reflection. This is explained and shown explicitly for n=4. Multiplication in D_8 is determined precisely using relations in D_8. This leads to a presentation of D_8, which readily generalizes for any n. 0:00 Review of internal semi-direct products 2:11 Dihedral groups 4:09 Dihedral group of order 8, D_8 6:48 Multiplication in D_8 #math #maths #grouptheory