Free group

Common card · No. 298211

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} ). The members of...

Read on Wikipedia · Image Original: Jakob.scholbach Vector: Pbroks13, CC BY-SA 3.0