We generlize Lemmas 7.3-7.7 from the Odd Order paper. Those lemmas we extend from p-solvable groups to pi-separable groups, where pi is an arbitrary set of primes. Note that even in the ease pi = {p} some of our results present proper generalizations. In some proofs we use the solvability of groups of odd order (in the case /pi/ < 3 our results do not depend on the solvability of groups of odd order). We give also very short (and, sometimes, new) proofs of some related known results, for example, Thompson's A x B-Lemma. Corollary 3 extends Lemma 8.2 of W. Felt and J. G. Thompson (Pacific J. Math. 13, 1963, 775-1029) from p-groups to solvable groups. (C) 1996 Academic Press, Inc. [References: 8]
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机译：我们从奇数顺序文件中得出7.3-7.7引理。这些引理从p可解组扩展到pi可分离组，其中pi是任意素数集。请注意，即使在pi = {p}的情况下，我们的某些结果也能给出适当的概括。在某些证明中，我们使用奇数组的可解性（在/ pi / <3的情况下，我们的结果不取决于奇数组的可解性）。我们还给出了一些相关的已知结果的非常简短（有时是新的）证明，例如Thompson's A x B-Lemma。推论3将W.Felt和J.G.Thompson（Pacific J.Math.13，1963，775-1029）的引理8.2从p组扩展到可解组。 （C）1996 Academic Press，Inc. [参考：8]
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