Group
A set
together with a special element
and with a
binary operation
-
is called a
group
when the following properties are fulfilled.
- The binary operation is associative, i.e., for all
,
we have
-

- The element
is a neutral element, i.e., for all
,
we have
-

- For every
,
there exists an inverse element, i.e., there exists some
such that
-
