Projective special linear group
= Projective special linear group
{title2=$PSL_n(F)=SL_n(F)/Z(SL_n(F))$}
The quotient of the <special linear group> by its scalar center, acting faithfully on <projective space>. It is a <simple group> for $n\ge3$, or for $n=2$ and $|F|>3$. <Elementary transvection matrices> give generation and perfectness, and the <Iwasawa simplicity lemma> applies to the abelian subgroup of transvections with a fixed center.