Subgroups of Z/One generator/Fact
Theorem about the subgroups of
Z
{\displaystyle {}\mathbb {Z} }
The
subgroups
of
Z
{\displaystyle {}\mathbb {Z} }
are precisely
the subsets of the form
Z
d
=
{
k
d
∣
k
∈
Z
}
,
{\displaystyle {}\mathbb {Z} d={\left\{kd\mid k\in \mathbb {Z} \right\}}\,,}
with a uniquely determined nonnegative number
d
{\displaystyle {}d}
.
Proof
,
Write another proof
are precisely
.