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The rank of a free group admitting a finite basis
Definition
A free group has finite rank if it admits a finite free basis. In that case its rank is
where is any finite free basis of . This is well-defined by Any two finite free bases of the same group have the same cardinality.
This definition is deliberately restricted to free groups that admit a finite free basis. It neither defines rank for a free group whose bases are infinite nor asserts that arbitrary infinite free bases have the same cardinality.
Depends on
Used by
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 50 results over 16 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.
Sources
- Encyclopedia of Mathematics, Free group (standard reference, not scraped)