]> 2026-07-24T19:52:15+00:00 Finite group 0 en 1 Term 2024-06-24T09:25:12Z 2460485.8925 Finite group 0 Finite group#DummitFoote;17;definition given as an additional comment after the formal definition of group 17 definition given as an additional comment after the formal definition of group 0 Finite group#AlperinBell;2 2 0 Finite group#Fraleigh;58;the term is not explicitly defined, but the definition is implicit in the section ''Finite groups and group tables'' 58 the term is not explicitly defined, but the definition is implicit in the section ''Finite groups and group tables'' 0 Finite group#Hungerford;24;definition introduced in paragraph, along with notion of order of a group 24 definition introduced in paragraph, along with notion of order of a group 0 Finite group#Gallian;56 56 0 Finite group#Herstein;28;definition introduced in paragraph 28 definition introduced in paragraph 0 1 table 2 [[Defining ingredient::Finite group]] Finite group# QUERY5656d24ffbdfff78a4e084787b8cf9de 0 2 table 5 [[Fact about:: <q>[[Page::Finite group]] [[Number::1]]</q> ]] Finite group# QUERY35ab646110b690c25fad3da2279a5bc7 0 2 table 3 [[Fact about.Page::Finite group]] Finite group# QUERY8a67e1f34a61166cfd6a3b93cb770980 0 1 table 2 [[Survey article about::Finite group]] Finite group# QUERY814a54e2124460d471bceaa89b82353d 0 2 plainlist 3 [[Survey article about.Defining ingredient::Finite group]] Finite group# QUERY184ea6d3ad12037b7815ee71b9166f6e 0 1 plainlist 2 [[Analogue of::Finite group]] Finite group# QUERY40b852f0b4401876cd3d89226fc2a6d8 0 1 plainlist 2 [[Variation of::Finite group]] Finite group# QUERY92afc20250ab514b1cec6fb94181f2aa 0 1 plainlist 2 [[Opposite of::Finite group]] Finite group# QUERYa1a4b2c939f153f31828734c907a906f 0 2 plainlist 4 [[Fact about.Page::Finite group]] [[Category:Group property implications]] Finite group# QUERYcf8e4f31e202f4cd146105b73e552005 0 2 plainlist 4 [[Fact about.Page::Finite group]] [[Category:Group property non-implications]] Finite group# QUERY919b968ee28b61433fe566066653b87c 0 2 plainlist 4 [[Fact about.Page::Finite group]] [[Category:Group metaproperty satisfactions]] Finite group# QUERY587821a5e1a9d3407a230e64848d4845 0 2 plainlist 4 [[Fact about.Page::Finite group]] [[Category:Group metaproperty dissatisfactions]] Finite group# QUERY43789b4a48f6baff3aab1d51ecd4bded 0 2 plainlist 4 [[Fact about.Page::Finite group]] [[Category:Group property satisfactions]] [[Category:Group property satisfactions]] [[Fact about.Page::Finite group]] Finite group# QUERYd3270686e13c8361b53c2f7ab8aae0e7 0 2 plainlist 4 [[Fact about.Page::Finite group]] [[Category:Group property dissatisfactions]] [[Category:Group property dissatisfactions]] [[Fact about.Page::Finite group]] Finite group# QUERYf4cfa618633b766d7293e26d32120444 0 1 table 2 [[Satisfies property::Finite group]] Finite group# QUERYf1665c5e0ee2e3b504e595b41dd93ca6 0 1 table 2 [[Dissatisfies property::Finite group]] Finite group# QUERY01602e642c9895a5bc4e61a9449611b9 0 1 list 4 [[Stronger than::Group of prime power order]] [[Weaker than::Finite group]] Finite group# QUERY22b7edc21bf6eaa73f39ec73d362d63b 0 1 broadtable 4 [[Stronger than::Group of prime power order]] [[Weaker than::Finite group]] Finite group# QUERY5071a7988770f495da7a894e571ef9b6 0 1 list 4 [[Stronger than::Odd-order group]] [[Weaker than::Finite group]] Finite group# QUERYa211e270c0f8c74c57073779a0bb0204 0 1 broadtable 4 [[Stronger than::Odd-order group]] [[Weaker than::Finite group]] Finite group# QUERY6a0a783226bea6c1601fdc28ee0c0675 0 1 list 4 [[Stronger than::Finite group]] [[Weaker than::Finite cyclic group]] Finite group# QUERYc8e1156cf9373f6235438dc3e074205a 0 1 broadtable 4 [[Stronger than::Finite group]] [[Weaker than::Finite cyclic group]] Finite group# QUERY7a4d22c6cb22ea2adf3080dce6772a89 0 1 list 4 [[Stronger than::Finite group]] [[Weaker than::Finite abelian group]] Finite group# QUERYf6e7ab78a084e648a277f818ab462d01 0 1 broadtable 4 [[Stronger than::Finite group]] [[Weaker than::Finite abelian group]] Finite group# QUERYb6d50a6c08fc01027fd906bbb214676b 0 1 list 4 [[Stronger than::Abelian group]] [[Weaker than::Finite abelian group]] Finite group# QUERY78382e8b8651f29844dc259dfe2de2c3 0 1 broadtable 4 [[Stronger than::Abelian group]] [[Weaker than::Finite abelian group]] Finite group# QUERYe5da314eaefee19391eb6d0fbf164380 0 1 list 4 [[Stronger than::Finite group]] [[Weaker than::Finite nilpotent group]] Finite group# QUERYcd2440011d869f8cc145c58f8d22ad70 0 1 broadtable 4 [[Stronger than::Finite group]] [[Weaker than::Finite nilpotent group]] Finite group# QUERY0a38a23929603509930fa3a6d98a2c9a 0 1 list 4 [[Stronger than::Nilpotent group]] [[Weaker than::Finite nilpotent group]] Finite group# QUERY4d9c09abd7a893fde7cc3a6ca80bc080 0 1 broadtable 4 [[Stronger than::Nilpotent group]] [[Weaker than::Finite nilpotent group]] Finite group# QUERY9a0674b0cedab2f95e2b19a9c41337fd 0 1 list 4 [[Stronger than::Finite group]] [[Weaker than::Finite solvable group]] Finite group# QUERYd12bc0c8cddd3c99a0c3429f309ed634 0 1 broadtable 4 [[Stronger than::Finite group]] [[Weaker than::Finite solvable group]] Finite group# QUERYe87bd58af5abacc261fef42bf0c6f7f8 0 1 list 4 [[Stronger than::Solvable group]] [[Weaker than::Finite solvable group]] Finite group# QUERY57e2926f2fbdd6630475f7aff7a8c702 0 1 broadtable 4 [[Stronger than::Solvable group]] [[Weaker than::Finite solvable group]] Finite group# QUERYf06e13e1bcf6c1cbea06803935439a42 0 1 list 4 [[Stronger than::Periodic group]] [[Weaker than::Finite group]] Finite group# QUERY9f4785fbf2176b150d84b7a072a81222 0 1 broadtable 4 [[Stronger than::Periodic group]] [[Weaker than::Finite group]] Finite group# QUERY3e1d91559eb806dd32d96adf28806068 0 1 list 4 [[Stronger than::Group of finite exponent]] [[Weaker than::Finite group]] Finite group# QUERY7a75e79270727b11f1faf6e775eb6010 0 1 broadtable 4 [[Stronger than::Group of finite exponent]] [[Weaker than::Finite group]] Finite group# QUERY2bb847ff33818e7f897a53bf1ffe7938 0 1 list 4 [[Stronger than::Finitely generated group]] [[Weaker than::Finite group]] Finite group# QUERY8d5af38212a4be77bee4c19395801acf 0 1 broadtable 4 [[Stronger than::Finitely generated group]] [[Weaker than::Finite group]] Finite group# QUERY9cd68fa361abc7ee16f61ff43b63079e 0 1 list 4 [[Stronger than::Locally finite group]] [[Weaker than::Finite group]] Finite group# QUERYdadec78901936f62f6e7e21035c153a7 0 1 broadtable 4 [[Stronger than::Locally finite group]] [[Weaker than::Finite group]] Finite group# QUERYa6e855164892165779ca253d6e8d46d8 0 1 list 4 [[Stronger than::Noetherian group]] [[Weaker than::Finite group]] Finite group# QUERYa5adef02de6785c04fcb2d25a11f976d 0 1 broadtable 4 [[Stronger than::Noetherian group]] [[Weaker than::Finite group]] Finite group# QUERYfd5107f65195a687cc79758fd056bb3e Cyclic group:Z2 0 en Cyclic group:Z2 Cyclic group:Z3 0 en Cyclic group:Z3 Symmetric group:S3 0 en Symmetric group:S3 Elementary abelian group:E25 0 en Elementary abelian group:E25 Direct product of Z5 and S3 0 en Direct product of Z5 and S3 Direct product of Z3 and D10 0 en Direct product of Z3 and D10 Cyclic group:Z30 0 en Cyclic group:Z30 Cyclic group:Z33 0 en Cyclic group:Z33 Cyclic group:Z35 0 en Cyclic group:Z35 Cyclic group:Z39 0 en Cyclic group:Z39 Cyclic group:Z45 0 en Cyclic group:Z45 Cyclic group:Z48 0 en Cyclic group:Z48 Elementary abelian group:E49 0 en Elementary abelian group:E49 Holomorph of Q8 0 en Holomorph of Q8 Quaternion group 0 en Quaternion group Cyclic group:Z71 0 en Cyclic group:Z71 Cyclic group:Z103 0 en Cyclic group:Z103 Cyclic group:Z107 0 en Cyclic group:Z107 Cyclic group:Z113 0 en Cyclic group:Z113 Cyclic group:Z61 0 en Cyclic group:Z61 Cyclic group:Z97 0 en Cyclic group:Z97 Cyclic group:Z73 0 en Cyclic group:Z73 Cyclic group:Z89 0 en Cyclic group:Z89 Cyclic group:Z11 0 en Cyclic group:Z11 Cyclic group:Z13 0 en Cyclic group:Z13 Cyclic group:Z17 0 en Cyclic group:Z17 Cyclic group:Z19 0 en Cyclic group:Z19 Cyclic group:Z23 0 en Cyclic group:Z23 Cyclic group:Z29 0 en Cyclic group:Z29 Cyclic group:Z31 0 en Cyclic group:Z31 Cyclic group:Z37 0 en Cyclic group:Z37 Cyclic group:Z41 0 en Cyclic group:Z41 Cyclic group:Z43 0 en Cyclic group:Z43 Cyclic group:Z47 0 en Cyclic group:Z47 Cyclic group:Z53 0 en Cyclic group:Z53 Cyclic group:Z59 0 en Cyclic group:Z59 Cyclic group:Z67 0 en Cyclic group:Z67 Cyclic group:Z79 0 en Cyclic group:Z79 Cyclic group:Z83 0 en Cyclic group:Z83 Dihedral group:D14 0 en Dihedral group:D14 Cyclic group:Z14 0 en Cyclic group:Z14 Cyclic group:Z15 0 en Cyclic group:Z15 Cyclic group:Z21 0 en Cyclic group:Z21 Cyclic group:Z22 0 en Cyclic group:Z22 Dihedral group:D22 0 en Dihedral group:D22 Cyclic group:Z25 0 en Cyclic group:Z25 Cyclic group:Z26 0 en Cyclic group:Z26 Dihedral group:D26 0 en Dihedral group:D26 Dicyclic group:Dic28 0 en Dicyclic group:Dic28 Cyclic group:Z28 0 en Cyclic group:Z28 Direct product of Z2 and Z14 0 en Direct product of Z2 and Z14 Projective special linear group:PSL(3,2) 0 en Projective special linear group:PSL(3,2) Alternating group:A4 0 en Alternating group:A4 SmallGroup(36,3) 0 en SmallGroup(36,3) Dihedral group:D8 0 en Dihedral group:D8 General affine group:GA(1,11) 0 en General affine group:GA(1,11) Cyclic group:Z46 0 en Cyclic group:Z46 Alternating group:A6 0 en Alternating group:A6 Symmetric group:S4 0 en Symmetric group:S4 Every finite group has a finite composition series 0 en Every finite group has a finite composition series Finite implies subnormal join property 0 en Finite implies subnormal join property Finite normal implies amalgam-characteristic 0 en Finite normal implies amalgam-characteristic 0 Every finite group has a finite composition series#Finite group;2# 7809f08dd2fcc687e92731f01cc6d1c4 0 Sylow normalizer implies weakly abnormal#Finite group# 578a5e94e076cf92c1a77ee8e27a1fd6 0 Frattini subgroup is nilpotent in finite#Finite group# 578a5e94e076cf92c1a77ee8e27a1fd6 0 Finite implies subnormal join property#Finite group;2# 7809f08dd2fcc687e92731f01cc6d1c4 0 Finite normal implies amalgam-characteristic#Finite group;2# 7809f08dd2fcc687e92731f01cc6d1c4 0 Central implies potentially verbal in finite#Finite group# 578a5e94e076cf92c1a77ee8e27a1fd6 0 Finite not implies composition factor-unique#Finite group;2# 7809f08dd2fcc687e92731f01cc6d1c4 0 Finite not implies composition factor-permutable#Finite group;2# 7809f08dd2fcc687e92731f01cc6d1c4 0 Periodic not implies locally finite#Finite group;2# 7809f08dd2fcc687e92731f01cc6d1c4 0 Sylow subgroups exist#Finite group;3# 0a08e80e0dacc98b98b876f1ad8a285d Satisfies property 132 en Satisfies property Uses property satisfaction of 132 en Uses property satisfaction of Page 132 en Page