As J.S.Rose noted in his book "A Course on Group Theory" : There is a section of GLn(F) which is isomorphic to PSLn(F), n≥1, F is a field"?. I ask that "What can this section be?" 



Groups GLn(F) and PSLn(F)
No clue about the book but there is no non-trivial homomorphism from PSL(2,5) to GL(2,5). Use MAGMA or GAP to check it if it is not clear to you.


