Finite normal subgroup
From Groupprops
This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): finite group
View a complete list of such conjunctions
Contents
Definition
A subgroup of a group is termed a finite normal subgroup if it is finite (as a group) and normal as a subgroup.
Examples
VIEW: subgroups satisfying this property | subgroups dissatisfying property normal subgroup | subgroups dissatisfying property finite group
VIEW: Related subgroup property satisfactions | Related subgroup property dissatisfactions
Relation with other properties
Stronger properties
Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|
normal subgroup of prime order | normal subgroup and its order is a prime number | |||
finite central subgroup | finite and a central subgroup | central implies normal | any of the finite examples for normal not implies central | |FULL LIST, MORE INFO |
finite characteristic subgroup | finite and a characteristic subgroup | any of the finite examples for normal not implies characteristic | |FULL LIST, MORE INFO | |
normal subgroup of finite group | normal and the whole group is finite | |FULL LIST, MORE INFO |