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Dihedral Groups - Semi-direct Products - Part 2
Автор: Dr. Cong
Загружено: 2020-05-19
Просмотров: 1253
Описание:
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
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