]> 2026-07-24T10:21:13+00:00 Nilpotent group 0 en tabular 2 Term 2021-12-27T02:11:46Z 2459575.5915046 Nilpotent group 0 Nilpotent group#DummitFoote;190;formal definition 190 formal definition 0 Nilpotent group#AlperinBell;103;definition in paragraph 103 definition in paragraph 0 Nilpotent group#RobinsonGT;122;formal definition 122 formal definition 0 Nilpotent group#RobinsonAA;174;formal definition 174 formal definition 0 Nilpotent group#Hungerford;100;definition in paragraph 100 definition in paragraph 0 Nilpotent group#Herstein;117 117 0 1 plainlist 2 [[Definition style::tabular]] Nilpotent group# QUERYa06e7f16fa3dc8cb712b7a1b798724eb 0 1 table 2 [[Satisfies property::Nilpotent group]] Nilpotent group# QUERY8a63be1d5656016ba47cb9e7aa08448f 0 1 table 2 [[Dissatisfies property::Nilpotent group]] Nilpotent group# QUERY28ec2a6bbc1d56bb5d82e658a038d1e4 0 2 plainlist 4 [[Category:Group property satisfactions]] [[Fact about.Page::Nilpotent group]] [[Fact about.Page::Nilpotent group]] [[Category:Group property satisfactions]] Nilpotent group# QUERY9556a0394f61c07f0c556ec2c7d4aedd 0 2 plainlist 4 [[Category:Group property dissatisfactions]] [[Fact about.Page::Nilpotent group]] [[Fact about.Page::Nilpotent group]] [[Category:Group property dissatisfactions]] Nilpotent group# QUERY63a26810cdeaa11a6dc88a8e8f571331 0 1 table 2 [[Defining ingredient::Nilpotent group]] Nilpotent group# QUERY68c87301441139dfee64f688417bc603 0 2 table 5 [[Fact about:: <q>[[Page::Nilpotent group]] [[Number::1]]</q> ]] Nilpotent group# QUERY0d64f08346218356de51fb3f5fb01203 0 2 table 3 [[Fact about.Page::Nilpotent group]] Nilpotent group# QUERYbdf736217bbff152d8cdbce52fca1457 0 1 table 2 [[Survey article about::Nilpotent group]] Nilpotent group# QUERYd7d98a743b87c3587bef013940e4c7ae 0 2 plainlist 3 [[Survey article about.Defining ingredient::Nilpotent group]] Nilpotent group# QUERY6a00ceb89d716ccd24c234a5c3163d4c 0 1 plainlist 2 [[Analogue of::Nilpotent group]] Nilpotent group# QUERYb0e5b1817afaaaf924ab126811547354 0 1 plainlist 2 [[Variation of::Nilpotent group]] Nilpotent group# QUERYbe28e2d95e3d85da4355d4039fb85654 0 1 plainlist 2 [[Opposite of::Nilpotent group]] Nilpotent group# QUERY1514e1b7a754af850a8baeace95a8ffa 0 2 plainlist 4 [[Fact about.Page::Nilpotent group]] [[Category:Group property implications]] Nilpotent group# QUERY9ba6da14b02dd404e445acf29df5a6e6 0 2 plainlist 4 [[Fact about.Page::Nilpotent group]] [[Category:Group property non-implications]] Nilpotent group# QUERY1b3ab4ed20ff9205f359a38b803a2055 0 2 plainlist 4 [[Fact about.Page::Nilpotent group]] [[Category:Group metaproperty satisfactions]] Nilpotent group# QUERY58d996cd8e553e30b55309c2b65252fd 0 2 plainlist 4 [[Fact about.Page::Nilpotent group]] [[Category:Group metaproperty dissatisfactions]] Nilpotent group# QUERYcd4f67ee406b365b9172a1abe5a66006 0 1 table 4 [[Satisfies property::Nilpotent group]] [[Dissatisfies property::Abelian group]] Nilpotent group# QUERY53fcb86163ad2d0b549abce64bde371a 0 1 list 4 [[Stronger than::Nilpotent group]] [[Weaker than::Abelian group]] Nilpotent group# QUERYc87a59860f665630ea0cb5a49dbc76ef 0 1 broadtable 4 [[Stronger than::Nilpotent group]] [[Weaker than::Abelian group]] Nilpotent group# QUERY9ffea0cee44f5ba0d97046bd6ebee80e 0 1 table 4 [[Satisfies property::Nilpotent group]] [[Dissatisfies property::Cyclic group]] Nilpotent group# QUERY10065294ed739e8cfdc37dc78a7866e9 0 1 list 4 [[Stronger than::Nilpotent group]] [[Weaker than::Cyclic group]] Nilpotent group# QUERYb28e07a4a99e52ec30c50f11ceff5efe 0 1 broadtable 4 [[Stronger than::Nilpotent group]] [[Weaker than::Cyclic group]] Nilpotent group# QUERY0365370ebba92ce40b37fa5da3b488f2 0 1 plainlist 4 [[Satisfies property::Nilpotent group]] [[Dissatisfies property::Group of prime power order]] Nilpotent group# QUERY7a2716cac79c2618a36b07a7a383bc07 0 1 list 4 [[Stronger than::Nilpotent group]] [[Weaker than::Group of prime power order]] Nilpotent group# QUERY8693539fdf3521a6940895fedd46f341 0 1 broadtable 4 [[Stronger than::Nilpotent group]] [[Weaker than::Group of prime power order]] Nilpotent group# QUERY673f2018f2cb89c34dd24359099b7642 0 1 plainlist 4 [[Satisfies property::Nilpotent group]] [[Dissatisfies property::Finite nilpotent group]] Nilpotent group# QUERY62ddd88c42d5051163c61d772f4e7e7a 0 1 list 4 [[Stronger than::Nilpotent group]] [[Weaker than::Finite nilpotent group]] Nilpotent group# QUERY4d9c09abd7a893fde7cc3a6ca80bc080 0 1 broadtable 4 [[Stronger than::Nilpotent group]] [[Weaker than::Finite nilpotent group]] Nilpotent group# QUERY9a0674b0cedab2f95e2b19a9c41337fd 0 1 table 4 [[Satisfies property::Nilpotent group]] [[Dissatisfies property::Group of nilpotency class two]] Nilpotent group# QUERY3236b5364a01fd37726d1eaee185600a 0 1 list 4 [[Stronger than::Nilpotent group]] [[Weaker than::Group of nilpotency class two]] Nilpotent group# QUERYf0089d3ea97a4e7bea379229e85b9cb6 0 1 broadtable 4 [[Stronger than::Nilpotent group]] [[Weaker than::Group of nilpotency class two]] Nilpotent group# QUERY0ce0c3026815a45e7766be316b3477be 0 1 list 4 [[Stronger than::Nilpotent group]] [[Weaker than::Aut-nilpotent group]] Nilpotent group# QUERY51083f3e465367be7f1f6c5107cddefc 0 1 broadtable 4 [[Stronger than::Nilpotent group]] [[Weaker than::Aut-nilpotent group]] Nilpotent group# QUERY4883dd73291d89994ee151c0ef0a3930 0 1 table 4 [[Satisfies property::Nilpotent group]] [[Dissatisfies property::UL-equivalent group]] Nilpotent group# QUERYa37438035fc6b12223debcd48453e0e9 0 1 list 4 [[Stronger than::Nilpotent group]] [[Weaker than::UL-equivalent group]] Nilpotent group# QUERY4f771142b4dc3b0588d5879a6297ae0a 0 1 broadtable 4 [[Stronger than::Nilpotent group]] [[Weaker than::UL-equivalent group]] Nilpotent group# QUERYbcf7d3d385fa92f787fd2fca8671ce9a 0 1 table 4 [[Satisfies property::Metanilpotent group]] [[Dissatisfies property::Nilpotent group]] Nilpotent group# QUERY3c76c9df31620df98609fe279d7533e4 0 1 list 4 [[Stronger than::Metanilpotent group]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERYec1817dcb68d0e26ec307958f201f852 0 1 broadtable 4 [[Stronger than::Metanilpotent group]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERYf799ad1776e6630ad75d9ca404f2c084 0 1 table 4 [[Satisfies property::Solvable group]] [[Dissatisfies property::Nilpotent group]] Nilpotent group# QUERY1d6956252bce12543c8c61e552216574 0 1 list 4 [[Stronger than::Solvable group]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERY95a94ea6a10732c14dd43030296dcc14 0 1 broadtable 4 [[Stronger than::Solvable group]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERYca958f78fa6def24495221dbebb98f6d 0 1 list 4 [[Stronger than::Group in which every maximal subgroup is normal]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERYf9584f7443547a65b5004a154c17b03a 0 1 broadtable 4 [[Stronger than::Group in which every maximal subgroup is normal]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERYdfbc89f5dc5b2e5895a667e8601b129a 0 1 list 4 [[Stronger than::Group in which every subgroup is subnormal]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERYd7d5b6b3eece74dd72e58c278d62d453 0 1 broadtable 4 [[Stronger than::Group in which every subgroup is subnormal]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERY19324041786716734611921f0ea6528d 0 1 list 4 [[Stronger than::Group satisfying normalizer condition]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERYd1888c6c1724bf2c6a77af0244a328c3 0 1 broadtable 4 [[Stronger than::Group satisfying normalizer condition]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERYfe0477f3f64cfb67e1ad36ccc9c22f9a 0 1 list 4 [[Stronger than::Hypercentral group]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERYb04a26ed2d55eef4fa00fc45a6911019 0 1 broadtable 4 [[Stronger than::Hypercentral group]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERY701d28602f4685823217bb05bba37aef 0 1 list 4 [[Stronger than::Hypocentral group]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERYaec43483871e5ccad290228a8998cd15 0 1 broadtable 4 [[Stronger than::Hypocentral group]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERY82c9525859b8f9e61007547960b7e3a2 0 1 list 4 [[Stronger than::Locally nilpotent group]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERY80f9e0984940d64550bba7a2b3794e71 0 1 broadtable 4 [[Stronger than::Locally nilpotent group]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERY45b2fe463e48916d600a238ea9629e36 0 1 list 4 [[Stronger than::Residually nilpotent group]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERYe47df42365db2b7c105fb2f7671fba6c 0 1 broadtable 4 [[Stronger than::Residually nilpotent group]] [[Weaker than::Nilpotent group]] Nilpotent group# QUERY9a2e4b3e1f3023941925cc61ffe231a0 0 1 plainlist 2 [[Obtained by applying::Diagonal-in-square operator]] Nilpotent group# QUERYa1136ba471c50b97991562a8e87bef2a Symmetric group:S3 0 en Symmetric group:S3 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 Dihedral group:D14 0 en Dihedral group:D14 Dihedral group:D22 0 en Dihedral group:D22 Dihedral group:D26 0 en Dihedral group:D26 Projective special linear group:PSL(3,2) 0 en Projective special linear group:PSL(3,2) Alternating group:A4 0 en Alternating group:A4 General affine group:GA(1,11) 0 en General affine group:GA(1,11) Alternating group:A6 0 en Alternating group:A6 Symmetric group:S4 0 en Symmetric group:S4 Cyclic group:Z2 0 en Cyclic group:Z2 Cyclic group:Z3 0 en Cyclic group:Z3 Elementary abelian group:E25 0 en Elementary abelian group:E25 Cyclic group:Z30 0 en Cyclic group:Z30 Elementary abelian group:E49 0 en Elementary abelian group:E49 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 Cyclic group:Z28 0 en Cyclic group:Z28 Direct product of Z2 and Z14 0 en Direct product of Z2 and Z14 Dihedral group:D8 0 en Dihedral group:D8 Nilpotent automorphism group implies nilpotent of class at most one more 0 en Nilpotent automorphism group implies nilpotent of class at most one more Abelian implies nilpotent 0 en Abelian implies nilpotent Prime power order implies nilpotent 0 en Prime power order implies nilpotent Nilpotent implies every nontrivial normal subgroup contains a cyclic normal subgroup 0 en Nilpotent implies every nontrivial normal subgroup contains a cyclic normal subgroup Nilpotent implies every subgroup is subnormal 0 en Nilpotent implies every subgroup is subnormal Nilpotent implies center is normality-large 0 en Nilpotent implies center is normality-large Local powering-invariant subgroup containing the center is intermediately local powering-invariant in nilpotent group 0 en Local powering-invariant subgroup containing the center is intermediately local powering-invariant in nilpotent group Abelian group 0 en Abelian group Cyclic group 0 en Cyclic group Dedekind group 0 en Dedekind group Solvable group 0 en Solvable group Engel group 0 en Engel group 0 Supersolvable implies nilpotent derived subgroup#Nilpotent group;3# d9ec3c48e0c93c5c221cd185ef12b8f7 0 Maximal among abelian normal implies self-centralizing in nilpotent#Nilpotent group# c2d60a8e10a819e9c97f18a5f171118d 0 Nilpotent implies normalizer condition#Nilpotent group# c2d60a8e10a819e9c97f18a5f171118d 0 Nilpotent implies every nontrivial normal subgroup contains a cyclic normal subgroup#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Nilpotent implies every subgroup is subnormal#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Nilpotent implies every maximal subgroup is normal#Nilpotent group# c2d60a8e10a819e9c97f18a5f171118d 0 Nilpotent implies center is normality-large#Nilpotent group;3# d9ec3c48e0c93c5c221cd185ef12b8f7 0 Nilpotent implies center is normality-large#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Nilpotent automorphism group implies nilpotent of class at most one more#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Nilpotent automorphism group implies nilpotent of class at most one more#Nilpotent group# c2d60a8e10a819e9c97f18a5f171118d 0 Nilpotent not implies ACIC#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 P-group not implies nilpotent#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Nilpotent not implies nilpotent automorphism group#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Abelian implies nilpotent#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Nilpotent not implies abelian#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 CA not implies nilpotent#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Prime power order implies nilpotent#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Solvable not implies nilpotent#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Locally nilpotent not implies nilpotent#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Supersolvable not implies nilpotent#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Nilpotent not implies UL-equivalent#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Rationally powered not implies nilpotent#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Nilpotent not implies generated by abelian normal subgroups#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Normalizer condition not implies nilpotent#Nilpotent group;2# bd9f0682e64cd2b1fd090d174ad979e2 0 Local powering-invariant subgroup containing the center is intermediately local powering-invariant in nilpotent group#Nilpotent group;3# d9ec3c48e0c93c5c221cd185ef12b8f7 Dissatisfies property 132 en Dissatisfies property Satisfies property 132 en Satisfies property Proves property satisfaction of 132 en Proves property satisfaction of Uses property satisfaction of 132 en Uses property satisfaction of Stronger than 132 en Stronger than Weaker than 132 en Weaker than Page 132 en Page