Noetherianness is subgroup-closed: Difference between revisions
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Any [[subgroup]] of a [[Noetherian group]] is [[Noetherian group]]. | Any [[subgroup]] of a [[Noetherian group]] is [[Noetherian group]]. | ||
==Related facts== | |||
===Similar facts=== | |||
* [[Noetherianness is quotient-closed]] | |||
* [[Noetherianness is extenion-closed]] | |||
* [[Artinianness is subgroup-closed]] | |||
===Opposite facts=== | |||
* [[Finitely generated not implies Noetherian]] shows that a subgroup of a finitely generated group need not be finitely generated. | |||
Latest revision as of 22:29, 6 February 2012
This article gives the statement, and possibly proof, of a group property (i.e., Noetherian group) satisfying a group metaproperty (i.e., subgroup-closed group property)
View all group metaproperty satisfactions | View all group metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for group properties
Get more facts about Noetherian group |Get facts that use property satisfaction of Noetherian group | Get facts that use property satisfaction of Noetherian group|Get more facts about subgroup-closed group property
Statement
Any subgroup of a Noetherian group is Noetherian group.
Related facts
Similar facts
Opposite facts
- Finitely generated not implies Noetherian shows that a subgroup of a finitely generated group need not be finitely generated.