Let A be a group acting on a solvable group G and let N be an A-invariant normal subgroup of G such that \([G,A]\nsubseteq N\). We prove the inequality \(h([G,A])\le h([G,A]N/N)+h([N,A])\) where h(G) denotes the Fitting height of G. As an application of this result, we obtain several Fitting height inequalities. A new concept “fixed point free separability” and a new characteristic subgroup Y(G) is defined and used in order to prove some further results about the Fitting height of a group. In the last section, a new characterization of solvable groups is given: a group G is solvable if and only if it is fixed point free separable.

让阿是作用于可解的基团G ^并让Ñ是阿的-invariant正常子群ģ使得\（[G，A] \ nsubseteqÑ\） 。我们证明了不等式\（H（[G，A]）\文件H（[G，A] N / N）+ H（[N，A]）\）其中ħ（ģ）表示的拟合高度ģ。作为此结果的应用，我们获得了几个拟合高度不等式。一个新概念“不动点可分离性”和一个新的特征子组Y（G定义和使用）是为了证明有关组拟合高度的其他结果。在最后一节中，给出了可溶基团的新表征：当且仅当基团G是无固定点可分离的时，基团G才是可溶的。