On the 2 out of 3 Lemma

Authors
Hethelyi, L Szoke, M
Citation
L. Hethelyi et M. Szoke, On the 2 out of 3 Lemma, COMM ALGEB, 27(6), 1999, pp. 2547-2553
Citations number
6
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN ALGEBRA
ISSN journal
00927872 → ACNP
Volume
27
Issue
6
Year of publication
1999
Pages
2547 - 2553
Database
ISI
SICI code
0092-7872(1999)27:6<2547:OT2OO3>2.0.ZU;2-N
Abstract
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. 6 8])?" We get a positive answer in two implications for p-nilpotent groups ( Section 2) and give some counterexamples in case of soluble groups (see Sec tion 3).