Cayley's theorem
Cayley's theorem puts all groups on the same footing, by considering any group (including infinite groups such as (R,+)) as a permutation group of some underlying set. Thus, theorems that are true for subgroups of permutation groups are true for groups in general. Nevertheless, Alperin and Bell note that "in general the fact that finite groups are imbedded in symmetric groups has not influenced the methods used to study finite groups".