Projective outer semilinear group

Definition
Let $$K$$ be a field and $$n$$ be a natural number. The projective outer semilinear group of degree $$n$$ over $$K$$, denoted $$PO\Gamma L(n,K)$$, is defined as the quotient group of the outer semilinear group $$O\Gamma L(n,K)$$ by the center of the general linear group $$GL(n,K)$$, which sits naturally as a subgroup of it.