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Abelian groupP-groupFinitely generated abelian groupTorsion groupTorsion subgroupDivisible groupLattice of subgroupsPerfect groupAlgebraic groupAbelian varietySimple groupAlgebraic posetGenerating set of a groupSolvable groupGraded ringCompact groupLinear algebraic groupNon-abelian groupPermutation groupSimple lie groupFree abelian groupFinitely generated groupSymmetric groupCyclic groupGroupArithmetic groupPolycyclic groupPartition of a setSumsetSpecial linear groupGeneral linear groupIncidence algebraFundamental groupInfinite groupCharacteristic subgroupPrimeTrivial groupPartially ordered setNormBandAffine groupInverse semigroupPower-associative algebraCayley's theoremSymmetric spaceCongruence subgroupAdelic algebraic groupG-moduleRank of a groupIdeal class groupCommutator subgroupGroup extensionGroup of lie typeResidually finite groupLength functionUpper and lower boundsFeit-thompson theoremSemigroupQuasigroupLinear groupWell-orderingOrthogonal groupGalois groupComplete graphConjugacy classEuclidean groupFundamental representationCharacter theoryClass field theoryAbelian von neumann algebraNormal subgroupSemisimple lie algebraWell-orderAlternating groupFinite groupAbelianizationPermutation graphSpecial linear lie algebraAtomComparison of topologiesFundamental theorem of arithmeticMatrix groupClass functionLie's third theoremBurnside's theoremIsogenyDiscrete groupGroup with operatorsGroup actionPrime elementSpecial unitary groupNilpotent groupComplete measureComponentPrimitive elementMonomial orderUnitary groupQuotient groupGrothendieck groupEuclid number