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Normal subgroupSimple groupLinear algebraic groupGalois groupTrivial groupFitting subgroupLinear groupAlgebraic groupAbelian groupFixed fieldSylow theoremGalois extensionChain groupPermutation groupSporadic groupStabilizer subgroupGroupCenterCyclic groupNormalizerDivision algebraTorsion subgroupMatrix groupQuotient groupHomology groupGalois theoryAlgebraic fundamental groupProfinite groupConjugacy classAutomorphism groupDirect productGroup theoryCycle groupLatticeChow groupSubgroupoidSupergroupSymmetric groupAnabelian geometryAlternative algebraExact sequenceCosetGroup functorHypergroupGroup actionSymmetry groupSemidirect productFundamental groupGeneral linear groupGroup ringBraid groupAffine groupCircle groupNoetherian moduleGalois fieldGrothendieck groupAlternating groupParatopological groupCayley's theoremPseudogroupAlgebraic closureModuleLie groupPrimitive elementAdditive groupAlgebraic subvarietyAbelianizationSpecial linear groupEuclidean groupQuasigroupRight cosetOrthogonal groupWeyl groupMalnormalityInverse semigroupFree groupIdealSemihypergroupSocleChain complexSurjunctive groupUnique factorization ringFree abelian groupRee groupTriangle groupSimple ringAlgebraCommutative algebraOrderCommutative ringSimple algebraQuotient ringTopological groupHyperalgebraFactor ringRight idealOrdered ringLoopIsomorphismCyclic number