  There were defined by R. Shwartz OGS for non-abelian groups, as an
interesting generalization of the basis of finite abelian groups. The
definition of OGS states that that every element of a group has a unique
presentation as a product of some powers of the OGS, in a specific given order.
In case of the symmetric groups S_{n} there is a paper of R. Shwartz, which
demonstrates a strong connection between the OGS and the standard Coxeter
presentation of the symmetric group. The OGS presentation helps us to find the
Coxeter length and the descent set of an arbitrary element of the symmetric
group. Therefore, it motivates us to generalize the OGS for the alternating
subgroup of the symmetric group, which we define in this paper. We generalize
also the exchange laws for the alternating subgroup, and we will show some
interesting properties of it.

Group Theory