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Symmetric groupGraph automorphismInner automorphismAffine groupGenerating set of a groupCommutator subgroupAutomorphism groupNormal subgroupCayley's theoremIsometry groupSymmetry groupGroupFundamental groupAutomorphismGroup actionPermutation groupSymmetric spaceCompact groupRegular representationBandGroup isomorphismHomomorphismIsogenyConjugacy classCharacter theoryLattice of subgroupsPerfect groupCosetNormInverse semigroupAutomorphic formAlgebraic groupPartition of a setLinear algebraic groupInfinite groupCongruence subgroupIdentity functorGeometric transformationPolycyclic groupEdge-transitive graphElementary abelian groupSubgroupSubcategoryMapping class groupGroup representationClass functionCyclic groupCovering groupFixed-point combinatorEuclidean groupGroup extensionFinitely generated groupKlein four-groupSurjective functionQuasigroupArithmetic groupIndicator functionDouble cosetPower-associative algebraAlternative algebraIrreducible representationFixed fieldTorsion groupAbelian groupCharacteristicRepresentation theoremComplementMorphismSolvable groupGrothendieck groupLie's third theoremMatrix groupCoverSymmetric graphFundamental representationWeyl groupTriangle groupTopological groupGroup ringOne-parameter groupGroup cohomologyCartan decompositionComplete measureClosureIncidence algebraAnalytic function of a matrixGraded ringBorel subgroupEndomorphismLinear groupIdentity morphismProjective unitary groupExact coverIdempotent matrixSemigroupExact sequenceCharacter tableSubmanifoldSpecial linear groupCohomology