Date: Thu, 19 Mar 1998 14:59:32 +0200 (IST) Reply-To: Assaf LibmanSubject: Endomorphisms of orthogonal groups I am interested in the following problem and would appreciate any hint or help. Let f an n-ary non-degenerate, positive definite quadratic form on the field of rational numbers Q. Let G=P\Omega_n(Q,f), namely G is the commutator subgroup of the orthogonal group O_n(Q,f) modulo its center. It is well known that for n>8, this group is simple. Is it true that any embedding G-->G is an automorphism ? (namely it is surjective). More generally, can one characterize the groups for which the endomorphisms ring consists only of their automorphisms and the trivial homomorphism ? Assaf Libman