Revision #523 → #1143 · back to history
addedCyclic group (lead)94b1c5d4a830
addedClassification of cyclic groups up to isomorphismbf9621321055
addedCyclic groups are abelian; finitely generated abelian groups are products of cyclic groups13f229d4feda
addedCyclic groups of prime order are simple7cf62ee98951
addedCyclic subgroup generated by g and order of an element25200f639843
addedCyclic group66b4e7b68b04
addedStandard finite cyclic group C_n97898692914d
addedComplex 6th roots of unity7dc7e0451c1f
addedInfinite cyclic groupc1efdae9fefd
addedMonogenous group (Bourbaki)d0ac0114100f
addedIntegers under addition96b7cd1490d9
addedIntegers modulo n under additionc5ff14238a03
addedGenerators of Z/nZ are units coprime to n29d6d5adcd61
addedZ/pZ as finite field F_p102a33eaae08
addedWhen (Z/nZ)^× is cyclicbddbb2ba6a20
addedPrimitive root modulo n8f13f3547d81
addedFinite subgroup of multiplicative group of a field is cyclic5dead11c2210
addedRotational symmetries of a polygon8fa5e2236303
addedCircle group is not cyclicb496d52cd692
addedn-th root of unityf7d0ff1bcf36
addedn-th roots of unity form a cyclic group4641c4d9a0eb
addedCyclic extension27dd6be947c1
addedGalois group of finite field extension is cyclicde9587e98deb
addedRealization of finite cyclic groups as Galois groups over finite fieldsdccca49d1a3e
addedSubgroups and quotients of cyclic groups are cyclic09411bf3c9eb
addedCyclic group is simple iff its order is prime8666d0670402
addedSubgroups of Z/nZ correspond to divisors of n46390e74d24f
addedEvery cyclic group is abeliane4c7aaccaa8d
addedPrimary cyclic groupaea6b23ba615
addedFundamental theorem of finitely generated abelian groups39a0471c82b1
addedConjugacy classes in a cyclic group7c11eb724994
addedNumber of elements of given order in Z/nZ54b2004d46cd
addedCharacterization of cyclic finite groups by elements of order dividing n01a479ad3953
addedOrder of element m in Z/nZ75fa123b6565
addedChinese remainder theorem for cyclic groups6af9abf77073
addedGroups of prime order are cyclic9dfb3b022465
addedCyclic numberba8a4555524f
addedGroup presentation of cyclic groupsd9a8c25263e4
addedEndomorphism ring of Z/nZb052665344f6
addedAutomorphism group of Z/nZdf0967e0dc04
addedEndomorphism ring of Z368ad8d7c99a
addedTensor product of cyclic groupsa7dcf2f8c9d1
addedHom group of cyclic groups14ae34250063
addedVirtually cyclic groupba0ae4e49beb
addedCharacterization of infinite virtually cyclic groups by ends0f3ae803766b
addedAbelian subgroups of hyperbolic groups are virtually cyclic8db886ea6264
addedProcyclic groupc3f7e84ba212
addedLocally cyclic group4c6629ad1e15
addedAdditive group of the rationals is locally cyclic19f7a51d47a6
addedLocally cyclic iff subgroup lattice is distributivee2c1f02e315a
addedCyclically ordered groupb9dfe20b2466
addedFinite subgroups of cyclically ordered groups are cyclica8a79dd3c709
addedMetacyclic group9412b065bd71
addedPolycyclic group9a1ef249f749
addedFinitely generated abelian and nilpotent groups are polycyclic3ac087f4db8c