Regular orbits of finite primitive solvable groups, II

Abstract

Suppose that a finite solvable group G acts faithfully, irreducibly and quasi-primitively on a finite vector space V. Then G has a uniquely determined normal subgroup E which is a direct product of extraspecial p-groups for various p and we denote e = | E / Z ( E ) | . We prove that when e = 5 , 6 , 7 , G will have regular orbits on V. This result, combined with a previous result of the author, will give a complete list of e such that G will have regular orbits on V.