Automorphism Group
As a vector space V has a basis {e1, ..., en} as described in the examples. If we take {v1, ..., vn} to be any n elements of V, then by linear algebra we have that the mapping T(ei) = vi extends uniquely to a linear transformation of V. Each such T can be considered as a group homomorphism from V to V (an endomorphism) and likewise any endomorphism of V can be considered as a linear transformation of V as a vector space.
If we restrict our attention to automorphisms of V we have Aut(V) = { T : V → V | ker T = 0 } = GLn(Fp), the general linear group of n × n invertible matrices on Fp.
Read more about this topic: Elementary Abelian Group
Famous quotes containing the word group:
“We begin with friendships, and all our youth is a reconnoitering and recruiting of the holy fraternity they shall combine for the salvation of men. But so the remoter stars seem a nebula of united light, yet there is no group which a telescope will not resolve; and the dearest friends are separated by impassable gulfs.”
—Ralph Waldo Emerson (1803–1882)