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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`
MSubgroupQ
​
MSubgroupQ
[group,subset]
checks whether
subset
forms a subgroup of
group
or not.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
Define a group using
FormMGroup
:
In[1]:=
G=
FormMGroup
[{0,1,2,3,4},Mod[#1+#2,5]&]
Out[1]=
MGroup
Operation: Binary
Order: 5

Take a subset:
In[2]:=
H={0,2}
Out[2]=
{0,2}
Check if it forms a subgroup or not:
In[3]:=
MSubgroupQ
[G,H]
Out[3]=
False
2

10
forms a subgroup of

10
In[4]:=
Z
10
=
MAdditiveGroup
[10]
Out[4]=
MGroup
Operation: Binary
Order: 10

In[5]:=
sub=
MElementPower

Z
10
,
MGroupDomain
[
Z
10
],2//DeleteDuplicates
Out[5]=
{0,2,4,6,8}
In[6]:=
MSubgroupQ
[
Z
10
,sub]
Out[6]=
True
RelatedGuides
▪
MGroups Package
""

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