Special affine group

Definition
Let $$n$$ be a natural number and $$k$$ be a field. The special affine group or affine special linear group of degree $$n$$ over $$k$$, denoted $$SA(n,k)$$, $$SA_n(k)$$, $$ASL(n,k)$$, or $$ASL_n(k)$$, is defined as the uses as intermediate construct::external semidirect product of the vector space $$k^n$$ by the defining ingredient::special linear group $$SL(n,k)$$.

It can be viewed as a subgroup of the general affine group, which is the semidirect product of the vector space with the whole general linear group.