Number of normal subgroups: Difference between revisions
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Let <math>G</math> be a [[group]]. The '''number of normal subgroups''' of <math>G</math> is the number of [[normal subgroup]]s that <math>G</math> has. | Let <math>G</math> be a [[group]]. The '''number of normal subgroups''' of <math>G</math> is the number of [[normal subgroup]]s that <math>G</math> has. | ||
==Related properties== | |||
A non-trivial group is said to be [[simple group|simple]] if it has precisely 2 normal subgroups, itself and the [[trivial group]]. | A non-trivial group is said to be [[simple group|simple]] if it has precisely 2 normal subgroups, itself and the [[trivial group]]. | ||
Latest revision as of 12:38, 15 January 2024
This article defines an arithmetic function on groups
View other such arithmetic functions
Definition
Let be a group. The number of normal subgroups of is the number of normal subgroups that has.
Related properties
A non-trivial group is said to be simple if it has precisely 2 normal subgroups, itself and the trivial group.