Projective outer semilinear group

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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.