We study the class of finite groups G satisfying class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316303155&_mathId=si1.gif&_user=111111111&_pii=S0021869316303155&_rdoc=1&_issn=00218693&md5=f8ec60eb613d2bbb60f3d3e4b94397e8" title="Click to view the MathML source">Φ(G/N)=Φ(G)N/Nclass="mathContainer hidden">class="mathCode"> for all normal subgroups N of G. As a consequence of our main results we extend and amplify a theorem of Doerk concerning this class from the soluble universe to all finite groups and answer in the affirmative a long-standing question of Christensen whether the class of finite groups which possess complements for each of their normal subgroups is subnormally closed.