- Bounded generation is unaffected by passing to a subgroup of finite index: if H is a finite index subgroup of G then G is boundedly generated if and only if H is boundedly generated.
- Any quotient group of a boundedly generated group is also boundedly generated.
- A finitely generated periodic group must be finite if it is boundedly generated; equivalently, an infinite finitely generated periodic group is not boundedly generated.
A pseudocharacter on a discrete group G is defined to be a real-valued function f on a G such that
- f(gh) − f(g) − f(h) is uniformly bounded and f(gn) = n·f(g).
- The vector space of pseudocharacters of a boundedly generated group G is finite dimensional.
Read more about this topic: Boundedly Generated Group
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Famous quotes containing the word properties:
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