Vipul: Created page with "{{wikilocal}} ==Definition== Let $k$ be a positive integer. A group is termed a '''locally $k$ -generated group''' if it satisfies the condition that ev..."

2012-02-14T08:31:36Z

Created page with "{{wikilocal}} ==Definition== Let <math>k</math> be a positive integer. A group is termed a '''locally <math>k</math>-generated group''' if it satisfies the condition that ev..."

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==Definition==

Let <math>k</math> be a positive integer. A group is termed a '''locally <math>k</math>-generated group''' if it satisfies the condition that every [[finitely generated group|finitely generated subgroup]] has a generating set of size at most <math>k</math>.

A group is termed '''locally boundedly generated''' if it is locally <math>k</math>-generated for some choice of <math>k</math>.

==Relation with other properties==

===Stronger properties===

{| class="sortable" border="1"
! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
|-
| [[Weaker than::finitely generated group]] || || || ||
|-
| [[Weaker than::locally cyclic group]] || || || ||
|}

Locally boundedly generated group - Revision history

Vipul: Created page with "{{wikilocal}} ==Definition== Let k be a positive integer. A group is termed a '''locally k-generated group''' if it satisfies the condition that ev..."

Vipul: Created page with "{{wikilocal}} ==Definition== Let $k$ be a positive integer. A group is termed a '''locally $k$ -generated group''' if it satisfies the condition that ev..."