In mathematics, the free group F S {\displaystyle F_{S}} over a given set S {\displaystyle S} consists of all words that can be built from members of S {\displaystyle S} , considering two words to be different unless their equality follows from the group axioms (e.g. s t = s u u − 1 t {\displaystyle st=suu^{-1}t} but s ≠ t − 1 {\displaystyle s\neq t^{-1}} for s , t , u ∈ S {\displaystyle s,t,u\in S} ).
In mathematics, the free group F S {\displaystyle F_{S}} over a given set S {\displaystyle S} consists of all words that can be built from members of S {\displaystyle S} , considering two words to be different unless their equality follows from the group axioms (e.g. s t = s u u − 1 t {\displaystyle st=suu^{-1}t} but s ≠ t − 1 {\displaystyle s\neq t^{-1}} for s , t , u ∈ S {\displaystyle s,t,u\in S} ).
Source: Wikipedia "Free group" · CC BY-SA 4.0
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