This article contains consequences that come from the
axioms of the group.
Consequences
Let
- be a group with a
binary operation
, that satisfies the axioms of the group. Then the following consequences from the axioms of the group are valid:
There is only one identity element
e_{G}
in the group.
For any element
there is only one single inverse element
.
For any elements
the equality
follows the equality
.
This consequence means that there may be a reduction in the group. In this case, we reduced both parts of the equality by the element
g.
For any elements
an equation of the type:
has only one solution:
.
For any elements
an equation of the type:
has only one solution:
.
For any elements
there is an inverse element
- for the product of elements:
g_{1}, g_{2}.