# Semantic search

(2,3,7)-triangle group, (2,3,7)-von Dyck group, 1-automorphism-invariant subgroup, 1-completed subgroup, 1-endomorphism-invariant subgroup, 1-isomorphic groups, 2-Engel group, 2-divisible group, 2-generated group, 2-hypernormalized subgroup, 2-locally finite group, 2-powered group, 2-sub-ideal of a Lie ring, 2-subnormal subgroup, 2-torsion-free group, 3-Engel group, 3-abelian group, 3-locally nilpotent group, 3-step group for a prime, 3-transposition group, 4-subnormal subgroup, A-group, ACU-closed group property, ACU-closed subgroup property, AEP-subgroup, APS homomorphism, APS of groups, Abelian direct factor, Abelian group, Abelian hereditarily normal subgroup, Abelian normal subgroup, Abelian normal subgroup of maximum order, Abelian subgroup, Abelian subgroup of maximum order, Abelian subgroup of maximum order which is normal, Abelian subgroup of maximum rank, Abelian-completed subgroup, Abelian-extensible automorphism, Abelian-extensible automorphism-invariant subgroup, Abelian-extensible endomorphism, Abelian-extensible endomorphism-invariant subgroup, Abelian-potentially characteristic subgroup, Abelian-potentially verbal subgroup, Abelian-quotient subgroup, Abelian-quotient-pullbackable automorphism-invariant subgroup, Abnormal subgroup, Absolutely normal subgroup, Absolutely regular p-group, Absolutely simple group, Action-isomorph-free subgroup, Algebra group, Algebraic automorphism, Algebraic subgroup, Algebraically closed group, Almost normal subgroup, Almost quasisimple group, Almost simple group, Almost subnormal subgroup, Alternating group, Alternating group:A10, Alternating group:A11, Alternating group:A12, Alternating group:A13, Alternating group:A14, Alternating group:A4, Alternating group:A5, Alternating group:A6, Alternating group:A7, Alternating group:A8, Alternating group:A9, Amalgam-characteristic subgroup, Amalgam-normal-subhomomorph-containing subgroup, Amalgam-strictly characteristic subgroup, Amalgamated free factor, Amalgamated free product of Z and Z over 2Z, Amalgamated free product of two copies of group of rational numbers over group of integers, Ambivalent group, Amenable discrete group, Approximate normalizer, Artinian group, Ascendant subgroup, Associated direct sum of a subnormal series, Asymptotically fixed-depth join-transitively subnormal subgroup, Auto-invariance property, Autoclinism-invariant subgroup, Automatic group, Automorph-commensurable subgroup, Automorph-conjugate subgroup, Automorph-dominating subgroup, Automorph-join-closed subnormal subgroup, Automorph-permutable subgroup, Automorphic subgroups, Automorphically endomorph-dominating subgroup, Automorphism group of a group, Automorphism group of alternating group:A6, Automorphism group of free group:F2, Automorphism of a group, Automorphism that preserves conjugacy classes for a generating set, Automorphism-faithful AEP-subgroup, Automorphism-faithful normal subgroup, Automorphism-faithful subgroup, BFC-group, BN-pair, Baby monster group, Baer Lie group, Baer Lie ring, Baer Malcev ring, Baer alternating loop ring, Baer diassociative loop, Baer group, Baer norm, Baer-Specker group, Balanced group, Balanced subgroup property (function restriction formalism), Balanced subgroup property (generic notion), Base diagonal of a wreath product, Base of a wreath product, Base of a wreath product with diagonal action, Basic Lie product, Baumslag-Solitar group:BS(1,2), Biautomatic group, Binary octahedral group, Binate group, Binilpotency, Bound-word subgroup, Bounded Engel group, Bounded-nilpotent IAPS, Bounded-solvable IAPS, Braid group:B3, Burnside group, Burnside group:B(2,4), Burnside group:B(2,6), Burnside group:B(4,3), C-closed normal subgroup, C-closed self-centralizing subgroup, C-closed subgroup, C-group, C-group (generating set sense), C-normal subgroup, C-subnormal subgroup, C1-group, CA-group, CCP-group, CDIN-subgroup, CEP-subgroup, CIA-group, CN-group, CS-Baer Lie group, CS-extensible automorphism, CS-pushforwardable automorphism, CSCFN-realizable group, Camina group, Canonically Lazard-dividable Lie ring, Canonically Lazard-divided Lie ring, Capable group, Carter subgroup, Center, Center of pronormal subgroup, Center-fixing automorphism, Center-fixing automorphism-balanced subgroup, Center-fixing automorphism-invariant subgroup, Centerless group, Centerless group that is upward-closed normal in its automorphism group, Central factor, Central factor of normalizer, Central factor-extensible automorphism, Central functor, Central product of D16 and Z4, Central product of D8 and Q8, Central product of D8 and Z12, Central product of D8 and Z16, Central product of D8 and Z4, Central product of D8 and Z8, Central product of M16 and Z8 over common Z2, Central product of SL(2,3) and Z4, Central product of SL(2,5) and SL(2,7), Central product of SL(2,5) and Z4, Central product of UT(3,3) and Z9, Central product of UT(3,Z) and Q, Central product of UT(3,Z) and Z identifying center with 2Z, Central product of Z9 and wreath product of Z3 and Z3, Central subgroup, Centralizer of involution, Centralizer-annihilating endomorphism-invariant subgroup, Centralizer-connected group, Centralizer-dense subgroup, Centralizer-free normal subgroup, Centralizer-free subgroup, Centralizer-large subgroup, Centrally closed subgroup, Centrally indecomposable group, Centrally large subgroup, Chain-extensible automorphism, Character-conjugate conjugacy classes, Characteristic AEP-subgroup, Characteristic central factor, Characteristic central subgroup, Characteristic closure, Characteristic core, Characteristic core of subgroup of finite index, Characteristic direct factor, Characteristic maximal subgroup of group of prime power order, Characteristic subgroup, Characteristic subgroup of center, Characteristic subgroup of direct factor, Characteristic subgroup of finite index, Characteristic subgroup-closed group property, Characteristic transitively normal subgroup, Characteristic-extensible automorphism, Characteristic-isomorph-free subgroup, Characteristic-potentially characteristic subgroup, Characteristic-semidirectly extensible automorphism, Characteristically DP-decomposable subgroup, Characteristically Hopfian group, Characteristically complemented characteristic subgroup, Characteristically complemented normal subgroup, Characteristically complemented subgroup, Characteristically metacyclic group, Characteristically metacylic group, Characteristically polycyclic group, Characteristically simple group, Characterization of free Lie ring in terms of eigenspaces of Dynkin operator, Chevalley group of type B:B3(3), Circle group, Class two Lie cring, Class two near-Lie cring, Class-inner automorphism, Class-inverting automorphism, Class-preserving automorphism, Class-separating field, Closure-characteristic subgroup, Co-Hopfian group, Cocentral subgroup, Cocentral subgroup of normalizer, Cofactorial automorphism, Cofactorial automorphism-invariant subgroup, Collection of groups satisfying a property-conditional congruence condition, Collection of groups satisfying a universal congruence condition, Collection of groups satisfying a universal non-divisibility condition, Combable group, Commutative binary operation, Commutator of a normal subgroup and a subset, Commutator-closed subgroup property, Commutator-in-center subgroup, Commutator-in-centralizer subgroup, Commutator-realizable group, Commutator-verbal subgroup, Complemented central factor, Complemented characteristic subgroup, Complemented fully invariant subgroup, Complemented homomorph-containing subgroup, Complemented isomorph-containing subgroup, Complemented normal subgroup, Complemented transitively normal subgroup, Complete group, Complete map, Completely divisibility-closed normal subgroup, Completely divisibility-closed subgroup, Completion-equivalent subgroups, Composition factor-permutable group, Composition factor-unique group, Composition operator, Composition series-unique group, Composition subgroup, Compressed subgroup, Con-Cos group, Congruence on a group, Conjugacy class, Conjugacy functor, Conjugacy-closed Hall subgroup, Conjugacy-closed characteristic subgroup, Conjugacy-closed normal subgroup, Conjugacy-closed subgroup, Conjugacy-determined subgroup, Conjugacy-separable group, Conjugate-commensurable subgroup, Conjugate-comparable subgroup, Conjugate-dense subgroup, Conjugate-join-closed subgroup property, Conjugate-join-closed subnormal subgroup, Conjugate-large subgroup, Conjugate-permutable subgroup, Conjugation-invariantly embedded normal subgroup, Conjugation-invariantly embedded subgroup, Conjugation-invariantly permutably complemented subgroup, Conjugation-invariantly relatively normal subgroup, Constructibly critical subgroup, Contracharacteristic subgroup, Contranormal subgroup, Conway group:Co0, Conway group:Co1, Conway group:Co2, Conway group:Co3, Coprime automorphism-faithful characteristic subgroup, Coprime automorphism-faithful normal subgroup, Coprime automorphism-faithful subgroup, Coprime automorphism-invariant normal subgroup, Coprime automorphism-invariant subgroup, Core-characteristic subgroup, Core-free 2-subnormal subgroup, Core-free group, Core-free permutable subgroup, Core-free subgroup, Core-free subnormal subgroup, Countable group, Countably free group, Coxeter group, Cring, Critical subgroup, Cutting subgroup, Cyclic group, Cyclic group:Z10, Cyclic group:Z12, Cyclic group:Z128, Cyclic group:Z16, Cyclic group:Z18, Cyclic group:Z2, Cyclic group:Z20, Cyclic group:Z24, Cyclic group:Z243, Cyclic group:Z27, Cyclic group:Z3, Cyclic group:Z32, Cyclic group:Z36, Cyclic group:Z4, Cyclic group:Z40, Cyclic group:Z5, Cyclic group:Z6, Cyclic group:Z64, Cyclic group:Z7, Cyclic group:Z8, Cyclic group:Z81, Cyclic group:Z9, Cyclic normal subgroup of finite group, Cyclic-center group, Cyclonormal subgroup, Cyclotomic group, DRC-subgroup, Dedekind group, Derived subgroup, Descendant subgroup, Diagonal subgroup of a direct power, Diagram-extensible automorphism, Dicyclic group, Dicyclic group:Dic12, Dicyclic group:Dic20, Dicyclic group:Dic24, Dihedral group, Dihedral group:D10, Dihedral group:D12, Dihedral group:D128, Dihedral group:D14, Dihedral group:D16, Dihedral group:D18, Dihedral group:D20, Dihedral group:D24, Dihedral group:D256, Dihedral group:D32, Dihedral group:D64, Dihedral group:D8, Direct factor, Direct factor of characteristic subgroup, Direct factor over central subgroup, Direct factor-preserving automorphism, Direct power-closed characteristic subgroup, Direct product of A4 and A4, Direct product of A4 and D8, Direct product of A4 and E8, Direct product of A4 and Q8, Direct product of A4 and S3, Direct product of A4 and V4, Direct product of A4 and Z2, Direct product of A4 and Z3, Direct product of A4 and Z4, Direct product of A4 and Z4 and Z2, Direct product of A4 and Z5, Direct product of A4 and Z8, Direct product of A5 and S3, Direct product of A5 and SL(2,7), Direct product of A5 and V4, Direct product of A5 and Z2, Direct product of A5 and Z4, Direct product of A5 and Z7, Direct product of A6 and Z2, Direct product of D12 and Z2, Direct product of D12 and Z3, Direct product of D16 and V4, Direct product of D16 and Z2, Direct product of D16 and Z3, Direct product of D16 and Z4, Direct product of D32 and Z2, Direct product of D8 and D8, Direct product of D8 and E8, Direct product of D8 and Q8, Direct product of D8 and S3, Direct product of D8 and V4, Direct product of D8 and Z2, Direct product of D8 and Z3, Direct product of D8 and Z4, Direct product of D8 and Z4 and Z2, Direct product of D8 and Z5, Direct product of D8 and Z6, Direct product of D8 and Z7, Direct product of Dic12 and Z2, Direct product of E16 and Z4, Direct product of E8 and Z3, Direct product of E8 and Z4, Direct product of M16 and V4, Direct product of M16 and Z2, Direct product of M16 and Z3, Direct product of M16 and Z4, Direct product of M27 and Z3, Direct product of M32 and Z2, Direct product of Q16 and V4, Direct product of Q16 and Z2, Direct product of Q16 and Z3, Direct product of Q16 and Z4, Direct product of Q32 and Z2, Direct product of Q8 and Q8, Direct product of Q8 and S3, Direct product of Q8 and V4, Direct product of Q8 and Z3, Direct product of Q8 and Z4, Direct product of Q8 and Z5, Direct product of S3 and Z3, Direct product of S3 and Z4, Direct product of S4 and V4, Direct product of S4 and Z2, Direct product of S4 and Z3, Direct product of S4 and Z4, Direct product of S4 and Z5, Direct product of S5 and V4, Direct product of S5 and Z2, Direct product of SD16 and V4, Direct product of SD16 and Z2, Direct product of SD16 and Z3, Direct product of SD16 and Z4, Direct product of SD32 and Z2, Direct product of SL(2,3) and V4, Direct product of SL(2,3) and Z2, Direct product of SL(2,3) and Z3, Direct product of SL(2,3) and Z4, Direct product of SL(2,5) and PSL(3,2), Direct product of SL(2,5) and SL(2,7), Direct product of SL(2,5) and Z2, Direct product of SmallGroup(16,13) and V4, Direct product of SmallGroup(16,13) and Z2, Direct product of SmallGroup(16,13) and Z4, Direct product of SmallGroup(16,3) and V4, Direct product of SmallGroup(16,3) and Z2, Direct product of SmallGroup(16,3) and Z3, Direct product of SmallGroup(16,3) and Z4, Direct product of SmallGroup(16,4) and V4, Direct product of SmallGroup(16,4) and Z2, Direct product of SmallGroup(16,4) and Z4, Direct product of SmallGroup(32,12) and Z2, Direct product of SmallGroup(32,13) and Z2, Direct product of SmallGroup(32,14) and Z2, Direct product of SmallGroup(32,2) and Z2, Direct product of SmallGroup(32,24) and Z2, Direct product of SmallGroup(32,27) and Z2, Direct product of SmallGroup(32,33) and Z2, Direct product of SmallGroup(32,4) and Z2, Direct product of SmallGroup(32,49) and Z2, Direct product of SmallGroup(32,50) and Z2, Direct product of Z and Z2, Direct product of Z10 and Z2, Direct product of Z16 and V4, Direct product of Z16 and Z2, Direct product of Z16 and Z4, Direct product of Z27 and E9, Direct product of Z27 and Z3, Direct product of Z27 and Z9, Direct product of Z32 and Z2, Direct product of Z4 and V4, Direct product of Z4 and Z2, Direct product of Z4 and Z4, Direct product of Z4 and Z4 and V4, Direct product of Z4 and Z4 and Z2, Direct product of Z4 and Z4 and Z4, Direct product of Z6 and Z2, Direct product of Z6 and Z3, Direct product of Z6 and Z4, Direct product of Z8 and D8, Direct product of Z8 and E8, Direct product of Z8 and V4, Direct product of Z8 and Z2, Direct product of Z8 and Z4, Direct product of Z8 and Z4 and V4, Direct product of Z8 and Z4 and Z2, Direct product of Z8 and Z8, Direct product of Z81 and Z3, Direct product of Z9 and E27, Direct product of Z9 and E9, Direct product of Z9 and Z3, Direct product of Z9 and Z9, Direct product of Z9 and Z9 and Z3, Direct product of finite groups, Direct product of group of rational numbers and group of rational numbers modulo integers, Direct product of holomorph of Z8 and Z2