Subgroups and cosets

Let us begin with an example and let us consider the group table of the symmetric group Sym₃. Recall from (20.10) that Sym₃ consists of the six elements id = ( 1 2 3 1 2 3 ) , σ 1 = ( 1 2 3 2 3 1 ) , σ 2 = ( 1 2 3 3 1 2 ) , τ 1 = ( 1 2 3 1 3 2 ) , τ 2 = ( 1 2 3 3 2 1 ) , τ 3 = ( 1 2 3 2 1 3 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136547/a57ae1f0-6f59-46bd-bbdd-35a521b486a1/content/eq2454.tif"/>