Bounds on real finite linear groups that preserve a symmetric or skew symmetric bilinear form

Abstract

Abstract We extend the results of our earlier work on Jordan-type bounds for finite subgroups of complex classical groups to real groups. The bounds that we obtain are related to our previous results by means of structural results for finite linear groups that we can generalise here to compact groups. For the real analogue of orthogonal groups, we take into account the signature of a real quadratic form to determine bounds in every case.