Difference between revisions of "Number of subgroups"

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(Created page with '{{arithmetic function}} ==Definition== Let <math>G</math> be a group. The '''number of subgroups''' of <math>G</math> is the number of subgroups that <math>G</math> has…')
 
 
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{{arithmetic function}}
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{{arithmetic function on groups}}
  
 
==Definition==
 
==Definition==

Latest revision as of 00:39, 20 August 2009

This article defines an arithmetic function on groups
View other such arithmetic functions

Definition

Let G be a group. The number of subgroups of G is the number of subgroups that G has.

Note that the number of subgroups of G is finite if and only if G is a finite group. For full proof, refer: Finitely many subgroups iff finite