LAUSR

Abstract In this paper we prove that for each integer of the form n = 4 ϖ (where ϖ is a prime between 17 and 73) at least one of the following groups: P Ω n ± ( F l s ) , PSO n ± ( F l s ) , PO n ± ( F l s ) or PGO n ± ( F l s ) is a Galois group of Q for almost all primes l and infinitely many integers s > 0 . This is achieved by making use of the classification of small degree representations of finite simple groups of Lie type in defining characteristic due to Lubeck and a previous result of the author on the image of the Galois representations attached to RAESDC automorphic representations of GL n ( A Q ) .