free groups

Noun

free group (plural free groups)

1. A group that has a presentation without relators; equivalently, a free product of some number of copies of ℤ.
   • Given a set S of "free generators" of a free group, let S⁻¹ be the set of inverses of the generators, which are in one-to-one correspondence with the generators (the two sets are disjoint), then let (S∪S⁻¹)^* be the Kleene closure of the union of those two sets. For any string w in the Kleene...