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- Most important/basic terms (importance rank one): Abelian group, Alternating group, Automorphism group of a group, Automorphism of a group, Center, Characteristic subgroup, Commutative binary operation, Congruence on a group, Conjugacy class, Cyclic group, Cyclic group:Z2, Cyclic group:Z3, Cyclic group:Z4, Direct factor, Endomorphism of a group, Euler totient function, External direct product, Finite group, Group, Group action, Group of integers, Group of prime order, Homomorphism of groups, Improper subgroup, Index of a subgroup, Injective homomorphism, Inner automorphism, Internal direct product, Isomorphic groups, Isomorphism of groups, Klein four-group, Left coset of a subgroup, Maximal subgroup, Multiplication table of a finite group, Nontrivial subgroup, Normal subgroup, Order of a group, Outer automorphism group, Proper characteristic subgroup, Proper normal subgroup, Proper subgroup, Quotient map, Right coset of a subgroup, Subgroup, Symmetric group, Symmetric group:S3, Trivial group
- Very important/basic terms (importance rank two)
- Somewhat important/basic terms (importance rank two)

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## Subcategories

This category has the following 15 subcategories, out of 15 total.