Changes

Jump to: navigation, search

Klein four-group

1,288 bytes removed, 22:28, 10 July 2010
Arithmetic functions
==Arithmetic functions==
{| class="wikitable" border="1"! Function !! Value !! Explanation|-| [[Order of a group|order]] || [[arithmetic function value::order of a group;4|4]] |||-| [[Exponent of a group|exponent]] || [[arithmetic function value::exponent of a group;2|2]] || Cyclic subgroup of order two.|-| [[nilpotency class]] || [[arithmetic function value::nilpotency class;1|1]] || The group is {abelian.|p-| [[derived length]] || [[arithmetic function value::derived length;1|1]] || The group is abelian.|-| [[Frattini length]] || [[arithmetic function value::Frattini length;1table|1]] || The group is elementary abelian.|-| [[Fitting length]] || [[arithmetic function value::Fitting length;1|1]] || The group is abelian, hence nilpotent.|-| [[minimum size of generating set]] || [[arithmetic function value::minimum size of generating set;underlying prime = 2|2]] || Elementary abelian of rank two.order = 4|-| [[subgroup rank of a group|subgroup rank]] || [[arithmetic function value::subgroup rank of a group;2|2]] || |order p-| [[max-length of a group|max-length]] || [[arithmetic function value::max-length of a group;log = 2|2]] |||-| [[Rank of a p-group|rank as p-group]] || [[arithmetic function value::rank of a p-group;2|exponent = 2]] || |-| [[Normal rank of a exponent p-group|normal rank]] || [[arithmetic function value::normal rank of a p-group;2|2]] || log = 1|-| [[characteristic rank of a p-group]] || [[arithmetic function value::characteristic rank of a p-group;2|= 2]] || |}}
==Group properties==
Bureaucrats, emailconfirmed, Administrators
38,822
edits

Navigation menu