Def A
subgroup of a
group G is
a subset of
G which is a group relative to the
operations
of
G.
Equivalently, a subset H of G is a subgroup
of G if and only if:
- (a) eG in H;
- (b) x,y in H ==> xy in H;
- (c) x in H ==> x-1 in H.
For example the even integers form a subgroup of the additive
group of the integers (Z,+).