Given a group G={g1, g2, ..gn} and a subgroup H={h1, h2, ... hm},

- right cosets are Hg1, Hg2.... Hgn
- left cosets are g1H, g2H.... gnH.

Two right cosets are either identical or disjoint. proof:
for h1, h2 in H /\ g1,g2 in G

h1g1=h2g2

<=> g1=h1^h2g2

=> Hg1=Hh1^h2g2=Hg2.

Remark: Right and left cosets may be different.

m distinct elements/coset /\ n elements/group => n/m cosets/group

source

jl@crush.caltech.edu index

normal_subgroup

group_division