1. ## Cosets

Let
S be a subgroup of the group G. Suppose that a, b belongs to G

satisfies
Sa = bS. Thus the left coset of S containing a equals the right coset

of
S containing b. Show that Sa = aS = bS = Sb.

2. Originally Posted by peteryellow

Let S be a subgroup of the group G. Suppose that a, b belongs to G satisfies Sa = bS. Thus the right coset of S containing a equals the left coset of S containing b.

Show that Sa = aS = bS = Sb.
from $Sa=bS,$ we get $a=bs,$ and $b=ta$ for some $s, t \in S.$ thus: $aS=bsS=bS=Sa=Sta=Sb.$