Division algebras with PSL(2, q)-Galois maximal subfields

If G is a finite group and k is a field, then G is k-admissible if there exists a G-Galois extension L/k such that L is a maximal subfield of a k-division algebra. We prove that PSL(2, 7) is k-admissible for any number field which either fails to contain root -1 or which has two primes lying over the dyadic prime. In addition, PSL(2, 11) is shown to be admissible over Q or any number field k with at least two extensions of the dyadic prime. Indeed, there exist infinitely many linearly disjoint admissible extensions for these groups, (C) toot Academic Press.