Dihedral Groups

1
Dihedral Groups

• Breaking it down

2
Kn when n 0 mod 4
If the generators are odd, then all even powers
of the generators are even. Then Kn contains a
cyclic group of order n/2.
1
2
3
8
? (12345678) ?2 (1357)(2468) ?3
(14725836) ?4 (15)(26)(37)(48) ?5
(16385274) ?6 (1753)(4286) ?7 (18765432)
7
4
5
6
3
Kn when n 0 mod 4
If the generators are odd, then all even powers
of the generators are even. Then Kn contains a
cyclic group of order n/2.
1
2
3
8
È (16)(25)(34)(78)
7
4
5
6