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Function Repository Resource:

 SubgroupQ

Source Notebook

Test if a group is a subgroup of another

Contributed by: Tessa Wildsmith

ResourceFunction["SubgroupQ"][group1,group2]

tests if group1 is a subgroup of group2.

Examples

Basic Examples (5) 

For the symmetric group:

In[1]:=
ResourceFunction["SubgroupQ"][SymmetricGroup[3], SymmetricGroup[5]]
Out[1]=

This case is not a subgroup:

In[2]:=
ResourceFunction["SubgroupQ"][CyclicGroup[3], CyclicGroup[5]]
Out[2]=

Permutations group:

In[3]:=
ResourceFunction["SubgroupQ"][ PermutationGroup[{Cycles[{{2, 7}, {5, 10}}], Cycles[{{1, 3, 5, 7, 9}, {2, 4, 6, 8, 10}}]}], PermutationGroup[{Cycles[{{5, 10}}], Cycles[{{1, 3, 5, 7, 9}, {2, 4, 6, 8, 10}}]}]]
Out[3]=

This case is not a subgroup:

In[4]:=
ResourceFunction["SubgroupQ"][ PermutationGroup[{Cycles[{{1, 2, 9}, {3, 4, 5}, {6, 7, 8}}], Cycles[{{1, 4, 7}, {2, 5, 8}, {3, 6, 9}}], Cycles[{{3, 4, 5}, {6, 8, 7}}]}], PermutationGroup[{Cycles[{{1, 3, 5, 7, 9}, {2, 4, 6, 8, 10}}], Cycles[{{1, 2, 9, 8}, {3, 6, 7, 4}, {5, 10}}]}]]
Out[4]=

A case for the dihedral group:

In[5]:=
ResourceFunction["SubgroupQ"][DihedralGroup[9], PermutationGroup[{Cycles[{{1, 4, 7}, {2, 8, 5}}], Cycles[{{1, 2, 3, 4, 5, 6, 7, 8, 9}}], Cycles[{{1, 8}, {2, 7}, {3, 6}, {4, 5}}]}]]
Out[5]=

Publisher

Enrique Zeleny

Version History

  • 1.0.0 – 30 November 2021

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