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A Fitting height lemma and its applications
Archiv der Mathematik ( IF 0.5 ) Pub Date : 2021-05-02 , DOI: 10.1007/s00013-021-01591-3
M. Yasir Kızmaz

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.



中文翻译:

拟合高度引理及其应用

是作用于可解的基团G ^并让Ñ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ħģ)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YG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。

更新日期:2021-05-03
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