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Week 6

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Exercise /
AreTheNaturalNumbersASubgroupOfTheIntegers
CyclicGroupsAreAbelian
TheSetOfSimpleShiftPermutationsOn26LettersIsIsomorphicToZ26
TheSubgroupsOfZAreNZ
TheSymmetricGroupOfDegreeNIsAGroup
Problem /
AffineEncryptionKeyIntroduction
CancellationLawsForGroups
CanWeUseDivisionToCreateAGroup
EisensteinsCriterion
HeisenbergMatrixGroup
InversesInGroups
IrreduciblesBehaveLikePrimeNumbers
ModPIrreducibilityTest
RationalRootTest
ReducibilityOverQImpliesReducibilityOverZ
ReducibilityTestForDegrees2And3
SpansOfPermutationsAreSubgroups
SubgroupsAreSubsetsThatAreClosedUnderProductsAndInverse
TheGCDTheoremProof
TheInverseInAFiniteGroupIsAPowerOfTheElement
TheProductOfPrimitivesIsPrimitive
WeKnowLeftPXRightIsMaximalIfAndOnlyIfPXIsIrreducible
ZNAndUNAreGroups
Solution /
AffineEncryptionKeyIntroductionJosh
CancellationLawsForGroupsJason
CanWeUseDivisionToCreateAGroupMikai
HeisenbergMatrixGroupJosh
InversesInGroupsJoey
PowersOfProductsInAnAbelianGroupLevi
SpansOfPermutationsAreSubgroupsBen
TheInverseInAFiniteGroupIsAPowerOfTheElementTyler
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