# Category:Terminology

From Groupprops

*If you are new to the site and are looking for something specific, it is much quicker to use the search bar.*

View terms by importance rank:

- 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, 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): Alternating group:A4, Alternating group:A5, Alternating group:A6, Complemented normal subgroup, Dihedral group:D8, Direct product of Z4 and Z2, Finitely generated group, Finitely presented group, Free group, Free group:F2, Group of nilpotency class two, Hall subgroup, Metabelian group, Metacyclic group, Nilpotent group, Normal Hall subgroup, Normal Sylow subgroup, Projective special linear group:PSL(3,2), Quaternion group, Retract, Simple group, Solvable group, Special linear group:SL(2,3), Special linear group:SL(2,5), Subnormal subgroup, Supersolvable group, Sylow subgroup, Symmetric group:S4, Symmetric group:S5
- Somewhat important/basic terms (importance rank three): Almost simple group, Alternating group:A7, Alternating group:A8, Ambivalent group, Automorph-conjugate subgroup, Binary octahedral group, Characteristically simple group, Dihedral group:D16, Direct product of A4 and Z2, Direct product of D8 and Z2, Direct product of S4 and Z2, Double cover of symmetric group:S5 of minus type, Double cover of symmetric group:S5 of plus type, General linear group:GL(2,3), Generalized quaternion group:Q16, Hopfian group, M16, Mathieu group:M10, Mathieu group:M9, Monolithic group, Noetherian group, Permutable subgroup, Projective general linear group:PGL(2,7), Projective general linear group:PGL(2,9), Projective special linear group:PSL(2,11), Projective special linear group:PSL(2,8), Pronormal subgroup, Quasisimple group, Rational group, Rationally powered group, Residually finite group, SQ-universal group, Semidihedral group:SD16, Special linear group:SL(2,7), Special linear group:SL(2,9), Symmetric group:S7

Navigate the subcategories to find the terms you are looking for.

For an unsorted list of *all* facts, click here.

## Subcategories

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