WEAK MAXIMALITY CONDITION AND POLYCYCLIC GROUPS

Authors
KIM YK RHEMTULLA AH
Citation
Yk. Kim et Ah. Rhemtulla, WEAK MAXIMALITY CONDITION AND POLYCYCLIC GROUPS, Proceedings of the American Mathematical Society, 123(3), 1995, pp. 711-714
Citations number
8
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
123
Issue
3
Year of publication
1995
Pages
711 - 714
Database
ISI
SICI code
0002-9939(1995)123:3<711:WMCAPG>2.0.ZU;2-E
Abstract
A group G is called strongly restrained if there exists an integer n s uch that [x((y))] be generated by n elements for all x, y in G. We sho w that a group G is polycyclic-by-finite if and only if G is a finitel y generated strongly restrained group in which every nontrivial finite ly generated subgroup has a nontrivial finite quotient. This provides a general setting for various results in soluble and residually finite groups that have appeared recently.