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GroupTheoryPaclet

Guides

  • Extra Group Theory Functionality

Symbols

  • CharacteristicSubgroupQ
  • CommutatorSubgroup
  • DerivedSeries
  • DerivedSubgroup
  • FindGroupIsomorphism
  • GroupAutomorphismGroup
  • GroupCenter
  • GroupConjugacyClasses
  • GroupDirectProduct
  • GroupMinimalGeneratingSet
  • GroupQ
  • InnerAutomorphismGroup
  • IsomorphicGroupsQ
  • NormalSubgroupQ
  • OuterAutomorphismGroup
  • PerfectGroupQ
  • QuotientGroup
DanielMcDonald`GroupTheoryPaclet`
OuterAutomorphismGroup
​
OuterAutomorphismGroup
[g]
finds the outer automorphism group of the group
g
.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
Find the outer automorphism group of the following group:
In[11]:=
OuterAutomorphismGroup
[PermutationGroup[{Cycles[{{1,2,3}}],Cycles[{{1,2,3},{5,6}}],Cycles[{{5,6}}],Cycles[{{2,3}}]}]]
Out[11]=
PermutationGroup[{Cycles[{}],Cycles[{{1,2}}]}]
SeeAlso
FindGroupIsomorphism
 
▪
GroupAutomorphismGroup
 
▪
InnerAutomorphismGroup
 
▪
QuotientGroup
RelatedGuides
▪
Extra Group Theory Functionality
""

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