Locally boundedly generated group

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Locally boundedly generated group, all facts related to Locally boundedly generated group) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

Definition

Let $k$ be a positive integer. A group is termed a locally $k$-generated group if it satisfies the condition that every finitely generated subgroup has a generating set of size at most $k$.

A group is termed locally boundedly generated if it is locally $k$-generated for some choice of $k$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
finitely generated group
locally cyclic group