Alternating group:A8

Definition
This group is defined in the following equivalent ways:


 * 1) It is the member of family::alternating group of degree eight, i.e., over a set of size eight.
 * 2) It is the member of family::projective special linear group of degree four over the field of two elements, i.e., $$PSL(4,2)$$. It is also the member of family::special linear group $$SL(4,2)$$, the member of family::projective general linear group $$PGL(4,2)$$, and the member of family::general linear group $$GL(4,2)$$.

This is one member of the smallest order pair of non-isomorphic finite simple non-abelian groups having the same order. The other member of this pair is projective special linear group:PSL(3,4).

Equivalence of definitions
The equivalence between the various definitions within (2) follows from isomorphism between linear groups over field:F2.