]> 2026-06-28T17:50:38+00:00 Cyclic group:Z2 0 en 1 2 Term 2023-12-15T21:23:53Z 2460294.3915857 Cyclic group:Z2 0 Cyclic group:Z2#Underlying prime of p-group;2 2 0 Cyclic group:Z2#Order of a group;2 2 0 Cyclic group:Z2#Prime-base logarithm of order;1 1 0 Cyclic group:Z2#Max-length of a group;1 1 0 Cyclic group:Z2#Chief length;1 1 0 Cyclic group:Z2#Composition length;1 1 0 Cyclic group:Z2#Exponent of a group;2 2 0 Cyclic group:Z2#Prime-base logarithm of exponent;1 1 0 Cyclic group:Z2#Frattini length;1 1 0 Cyclic group:Z2#Minimum size of generating set;1 1 0 Cyclic group:Z2#Subgroup rank of a group;1 1 0 Cyclic group:Z2#Rank of a p-group;1 1 0 Cyclic group:Z2#Normal rank of a p-group;1 1 0 Cyclic group:Z2#Characteristic rank of a p-group;1 1 0 Cyclic group:Z2#Nilpotency class;1 1 0 Cyclic group:Z2#Derived length;1 1 0 Cyclic group:Z2#Fitting length;1 1 0 Cyclic group:Z2#Number of conjugacy classes;2 2 0 Cyclic group:Z2#Number of subgroups;2 2 0 Cyclic group:Z2#Number of conjugacy classes of subgroups;2 2 0 Cyclic group:Z2#Number of equivalence classes under real conjugacy;2 2 0 Cyclic group:Z2#Number of equivalence classes under rational conjugacy;2 2 0 Cyclic group:Z2#2;1 2 1 0 1 plainlist 2 [[Specific information about::Cyclic group:Z2]] Cyclic group:Z2# QUERYb64e7ba83dccdba9568bbc24db639f49 0 2 plainlist 3 [[Fact about.Page::Cyclic group:Z2]] Cyclic group:Z2# QUERY4d283774fe941ad75ddb82f61e7f4e98 0 2 plainlist 4 [[Fact about.Page::Cyclic group:Z2]] [[Category:Group property satisfactions]] Cyclic group:Z2# QUERYb013061d3e866d6d94ed26cfc3b90dbf 0 2 plainlist 4 [[Fact about.Page::Cyclic group:Z2]] [[Category:Subgroup property satisfactions]] Cyclic group:Z2# QUERYb3f01d926cfa71098e7f3a612c77e50c 0 2 plainlist 4 [[Fact about.Page::Cyclic group:Z2]] [[Category:Group property dissatisfactions]] Cyclic group:Z2# QUERY3043026e3c8ba815d8b603f817d883b8 0 1 plainlist 4 [[Page class::Term]] [[Particular example::Cyclic group:Z2]] Cyclic group:Z2# QUERYbd8a7fd3884cc4c46783b43bdaaca079 0 1 plainlist 3 [[Particular example::Cyclic group:Z2]] [[Category:Group properties]] Cyclic group:Z2# QUERYa4a70ab943a330458dce7ca0c50db2fd 0 1 plainlist 3 [[Particular example::Cyclic group:Z2]] [[Category:Subgroup properties]] Cyclic group:Z2# QUERY83a1383c0593ab8a6a503613dbf0232a 0 1 plainlist 4 [[Particular example::Cyclic group:Z2]] [[Page class::Fact]] Cyclic group:Z2# QUERY2a901353adca70ff0361ae9c63b8e2ec 0 1 plainlist 3 [[Particular example::Cyclic group:Z2]] [[Category:Group property non-implications]] Cyclic group:Z2# QUERY37fdc181e2be7edbfabb6cdf9f7ab767 0 1 plainlist 3 [[Particular example::Cyclic group:Z2]] [[Category:Subgroup property non-implications]] Cyclic group:Z2# QUERY91f6666d1d2fe257676029391d91966f 0 1 plainlist 3 [[Particular example::Cyclic group:Z2]] [[Category:Group metaproperty dissatisfactions]] Cyclic group:Z2# QUERYf6634179ef272f9c5f2a0868fd6150f0 0 1 plainlist 3 [[Particular example::Cyclic group:Z2]] [[Category:Subgroup metaproperty dissatisfactions]] Cyclic group:Z2# QUERY0b6138ab7f4d43829d1a915d8c5e6d0b 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERY3a67de97ce511db6299578f62e09f029 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERY6ea5c077bc97d25e4eb48aed355d3784 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Exponent of a group]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERY9aea2775927fdd85b5b89c7aa3f923f7 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Exponent of a group]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERY8c3bea0e36371df588fd11c5da3e61e7 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Exponent of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERY100ec1ff81251cd053b5d64bd17cfa6c 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of exponent]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERYe6cac204bad0a3460cdb2e16f9ada9f2 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of exponent]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERY293395ddc288e9cd58c5ca1816292d33 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of exponent]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERY4c1f2e280b208f6f9f0fddd77ae87ddb 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Frattini length]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERY206217d61ff02ae7b3133c5588213cce 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Frattini length]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERYc97cac1f808340611547748f41941823 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Frattini length]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERY3c6b993c49d03cfb6e2d4956d672a7a4 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Minimum size of generating set]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERY230e8aa990a4318395e2637c19304995 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Minimum size of generating set]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERYec93d74d1f07b00354996d5b23184aba 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Minimum size of generating set]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERY49b5ab64a97d7f6fc330483cb426c036 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Subgroup rank of a group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERYeeb11e2097eabb3b953b215d1dbb378d 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Subgroup rank of a group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERY0091efdd97b9090d1f2f2a24d3b16127 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Subgroup rank of a group]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERY34454195f8f2791153ebb290f8bcd6ea 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Rank of a p-group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERYd866c0155d1ef60c777b951f2b01ce80 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Rank of a p-group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERY5d57fc3c65d7cb34f4e343f28b202254 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Rank of a p-group]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERYd65fed11302674b9df97d1deff586a48 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Normal rank of a p-group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERY0229a64d503ca5a9f91b4b733c053a9c 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Normal rank of a p-group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERY9d9bd395e3e435e38e86d2ec58163980 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Normal rank of a p-group]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERYb2316714cd5b623271a238c70af90e1e 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Characteristic rank of a p-group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERY669b085e000bd641e375ebb0535e7df2 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Characteristic rank of a p-group]] [[Number::1]]</q> ]] [[Arithmetic function value:: <q>[[Page::Prime-base logarithm of order]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERY2b4d4811c88ee8615df02d08ebdd4178 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Characteristic rank of a p-group]] [[Number::1]]</q> ]] Cyclic group:Z2# QUERY37c9612d33f64cebf0b3fea5d32afd85 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERYb20b310494e481d3fabdef5aacb839de 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERYb4c99c1b821e11ac25d84be9ad91fd5e 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of subgroups]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERYc5531f2d1b775302eed4ee9ba4a7099c 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of subgroups]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERYc6f06b5179b28e4fc386646b5898cc5c 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of subgroups]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERYd220e11876d1135cad86ee44f9d60457 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of conjugacy classes of subgroups]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERY322871afe7f2b371b8fb8272167ac116 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under real conjugacy]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERY4a812b2e735ac02a0308bc275c76f8d4 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under real conjugacy]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERY7175b50b08553b741dbbe4710f77794f 0 2 table 10 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under rational conjugacy]] [[Number::2]]</q> ]] [[Arithmetic function value:: <q>[[Page::Order of a group]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERYc9d25ce59b8289657585bd1ee4aee9d7 0 2 table 5 [[Arithmetic function value:: <q>[[Page::Number of equivalence classes under rational conjugacy]] [[Number::2]]</q> ]] Cyclic group:Z2# QUERYd90cfc0c840e31bd763cde326262aec7 0 0 plainlist 1 [[:Groups of order 2]] Cyclic group:Z2# QUERY2227adcd647787e16878b3583768fc1e Normality is not transitive 0 en Normality is not transitive Homomorph-containing not implies no nontrivial homomorphism to quotient group 0 en Homomorph-containing not implies no nontrivial homomorphism to quotient group Direct product of Z2 and Z14 0 en Direct product of Z2 and Z14 Center of dihedral group:D8 0 en Center of dihedral group:D8 Second cohomology group for trivial group action of V4 on Z2 0 en Second cohomology group for trivial group action of V4 on Z2 Second cohomology group for trivial group action of Z2 on Z2 0 en Second cohomology group for trivial group action of Z2 on Z2 Second cohomology group for trivial group action of Q8 on Z2 0 en Second cohomology group for trivial group action of Q8 on Z2 Second cohomology group for trivial group action of direct product of Z4 and Z2 on Z2 0 en Second cohomology group for trivial group action of direct product of Z4 and Z2 on Z2 Second cohomology group for trivial group action of Z4 on Z2 0 en Second cohomology group for trivial group action of Z4 on Z2 Second cohomology group for trivial group action of D8 on Z2 0 en Second cohomology group for trivial group action of D8 on Z2 Second cohomology group for trivial group action of Z4 on Z2 0 en Second cohomology group for trivial group action of Z4 on Z2 Particular example 132 en Particular example Defining ingredient 132 en Defining ingredient Subgroup part 132 en Subgroup part Specific information about 132 en Specific information about Value 132 en Value