Soluble and locally soluble skew linear groups (Q1079667)

We study primitive skew linear groups that are soluble or locally soluble. Unlike the linear case, examples show that little can be said at the group level. Here we show that they are all extensions of groups in certain crossed products by certain locally finite groups of finite exponent. If the group is locally nilpotent stronger conclusions follow from weaker hypotheses. We also give some applications to absolutely irreducible groups.