Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
DanielMcDonald`GroupTheoryPaclet`
FindGroupIsomorphism  |
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Details and Options
Examples
(6)
Basic Examples
(3)
Find an isomorphism between two groups:
In[1]:=
 | FindGroupIsomorphism |
Out[1]=
{{1,8,2,7,9,3,10,4,6,11,5,12}}
Find three isomorphisms between two Abelian groups:
In[1]:=
| FindGroupIsomorphism |
Out[1]=
{Cycles[{}]Cycles[{}],Cycles[{{3,4,5}}]Cycles[{{1,2,3}}],Cycles[{{3,5,4}}]Cycles[{{1,3,2}}],Cycles[{{1,2}}]Cycles[{{4,5}}],Cycles[{{1,2},{3,4,5}}]Cycles[{{1,2,3},{4,5}}],Cycles[{{1,2},{3,5,4}}]Cycles[{{1,3,2},{4,5}}],Cycles[{}]Cycles[{}],Cycles[{{3,4,5}}]Cycles[{{1,3,2}}],Cycles[{{3,5,4}}]Cycles[{{1,2,3}}],Cycles[{{1,2}}]Cycles[{{4,5}}],Cycles[{{1,2},{3,4,5}}]Cycles[{{1,3,2},{4,5}}],Cycles[{{1,2},{3,5,4}}]Cycles[{{1,2,3},{4,5}}]}
Find all automorphisms of the symmetric group of degree four:
In[1]:=
| FindGroupIsomorphism |
Out[1]=
{Cycles[{}],Cycles[{{3,6},{4,5},{9,12},{10,11},{13,20},{14,19},{15,22},{16,21},{17,24},{18,23}}],Cycles[{{3,15},{4,16},{5,21},{6,22},{9,13},{10,14},{11,19},{12,20},{17,24},{18,23}}],Cycles[{{3,22},{4,21},{5,16},{6,15},{9,20},{10,19},{11,14},{12,13}}],Cycles[{{2,3},{4,5},{7,22},{8,24},{9,21},{10,19},{11,23},{12,20},{13,16},{14,18}}],Cycles[{{2,3,6},{7,22,15},{8,24,17},{9,20,16},{10,23,14},{11,19,18},{12,21,13}}],Cycles[{{2,3,7,22},{4,9,12,16},{5,13,20,21},{6,15},{8,24},{11,18,14,23}}],Cycles[{{2,3,15},{4,13,21},{5,9,16},{6,7,22},{8,24,17},{10,18,11},{14,19,23}}],Cycles[{{2,6,3},{7,15,22},{8,17,24},{9,16,20},{10,14,23},{11,18,19},{12,13,21}}],Cycles[{{2,6},{4,5},{7,15},{8,17},{9,13},{10,18},{11,14},{12,16},{19,23},{20,21}}],Cycles[{{2,6,22},{3,7,15},{4,12,21},{5,20,16},{8,17,24},{10,11,23},{14,18,19}}],Cycles[{{2,6,7,15},{3,22},{4,20,13,16},{5,12,9,21},{8,17},{10,23,19,18}}],Cycles[{{2,7},{4,13},{5,9},{6,15},{10,19},{12,21},{16,20},{18,23}}],Cycles[{{2,7},{3,6,22,15},{4,20,21,9},{5,12,16,13},{10,14,19,11},{17,24}}],Cycles[{{2,7},{3,15,22,6},{4,9,21,20},{5,13,16,12},{10,11,19,14},{17,24}}],Cycles[{{2,7},{3,22},{4,12},{5,20},{9,16},{11,14},{13,21},{18,23}}],Cycles[{{2,15,3},{4,21,13},{5,16,9},{6,22,7},{8,17,24},{10,11,18},{14,23,19}}],Cycles[{{2,15},{4,9},{5,13},{6,7},{8,17},{10,23},{11,14},{12,20},{16,21},{18,19}}],Cycles[{{2,15,22},{3,7,6},{4,13,12},{5,9,20},{8,17,24},{10,14,18},{11,23,19}}],Cycles[{{2,15,7,6},{3,22},{4,16,13,20},{5,21,9,12},{8,17},{10,18,19,23}}],Cycles[{{2,22,7,3},{4,16,12,9},{5,21,20,13},{6,15},{8,24},{11,23,14,18}}],Cycles[{{2,22,15},{3,6,7},{4,12,13},{5,20,9},{8,24,17},{10,18,14},{11,19,23}}],Cycles[{{2,22},{3,7},{4,20},{5,12},{8,24},{9,13},{10,19},{11,18},{14,23},{16,21}}],Cycles[{{2,22,6},{3,15,7},{4,21,12},{5,16,20},{8,24,17},{10,23,11},{14,19,18}}]}
Properties & Relations
(3)
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