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algebra
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groups
Dihedral Group
A dihedral group
D
n
is a group of order
2
n
containing an element
a
of order
n
and an element
b
of order
2
such that
b
a
b
=
a
−
1
Elements of a Dihedral Group
Suppose that
D
n
is a dihedral group, then it's elements are given by
{
e
,
a
1
,
a
2
,
…
,
a
n
−
1
,
b
e
,
b
a
1
,
b
a
2
,
…
,
b
a
n
−
1
}
show proof
Caley Table for D _ 4
A
B
C
D
E
F
G
H
A
A
B
C
D
E
F
G
H
B
B
C
D
A
H
G
E
F
C
C
D
A
B
F
E
H
G
D
D
A
B
C
G
H
F
E
E
E
G
F
H
A
C
B
D
F
F
H
E
G
C
A
D
B
G
G
F
H
E
D
B
A
C
H
H
E
G
F
B
D
C
A
show proof