Boundedly Generated Group - Definitions

Definitions

A group G is called boundedly generated if there exists a finite subset S of G and a positive integer m such that every element g of G can be represented as a product of at most m powers of the elements of S:

where and are integers.

The finite set S generates G, so a boundedly generated group is finitely generated.

An equivalent definition can be given in terms of cyclic subgroups. A group G is called boundedly generated if there is a finite family C1, …, CM of not necessarily distinct cyclic subgroups such that G = C1CM as a set.

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