On the 2 out of 3 lemma

摘要

In this paper, we examine the following question:do two conditions imply the third one in the '2 out of 3' Lemma (see e.g. Lemma 9.5 in Alp86, p. 68)?We get a positive answer in two implications for p-nilpotent groups (Section 2) and give some counterexamples in case of soluble groups (see Section 3).