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Wolfram Language
MGroups
Guides
MGroups Package
Symbols
FormMAction
FormMGroup
MAbelianQ
MAction
MAdditiveGroup
MAutomorphism
MCayleyGraph3D
MCayleyGraph
MCayleyTable
MCoset
MCycleForm
MCyclicQ
MDihedralGroup
MEDP
MElementCentralizer
MElementInverse
MElementOrbit
MElementOrder
MElementPower
MElementStabilizer
MFactorGroup
MGenerateSubgroup
MGroupCenter
MGroupDomain
MGroupIdentity
MGroup
MGroupOrder
MHomomorphism
MInnerAutomorphism
MInversesTable
MIsomorphism
MKernelAction
MKlein4Group
MMorphismKernel
MMultiplicativeGroup
MNormalSubgroupQ
MNormalSubgroups
MonoidQ
MPermutationRepresentation
MPermutationsGroup
MQuaternionGroup
MSubgroupLattice3D
MSubgroupLattice
MSubgroupQ
MSubgroups
MTuple
MVisualiseMorphism
SemiGroupQ
Taggar`MGroups`
M
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M
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]
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Examples
(
1
)
Basic Examples
(
1
)
For any group G:
I
n
[
1
]
:
=
G
=
M
D
i
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d
r
a
l
G
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o
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p
[
4
]
O
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t
[
1
]
=
M
G
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O
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i
o
n
:
B
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O
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:
8
Find the subgroup generated by
e
l
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m
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t
s
:
I
n
[
2
]
:
=
e
l
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m
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n
t
s
=
{
"
r
0
"
,
"
r
2
"
}
O
u
t
[
2
]
=
{
r
0
,
r
2
}
I
n
[
3
]
:
=
M
G
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n
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r
a
t
e
S
u
b
g
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o
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p
[
G
,
e
l
e
m
e
n
t
s
]
O
u
t
[
3
]
=
{
r
0
,
r
2
}
or by a single element:
I
n
[
4
]
:
=
M
G
e
n
e
r
a
t
e
S
u
b
g
r
o
u
p
[
G
,
"
r
1
"
]
O
u
t
[
4
]
=
{
r
0
,
r
1
,
r
2
,
r
3
}
R
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a
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e
d
G
u
i
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s
▪
M
G
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p
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P
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