SUBNORMAL SUBGROUPS OF GROUP-RING UNITS

Authors
MARCINIAK ZS SEHGAL SK
Citation
Zs. Marciniak et Sk. Sehgal, SUBNORMAL SUBGROUPS OF GROUP-RING UNITS, Proceedings of the American Mathematical Society, 126(2), 1998, pp. 343-348
Citations number
14
Categorie Soggetti
Mathematics,Mathematics,Mathematics,Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
126
Issue
2
Year of publication
1998
Pages
343 - 348
Database
ISI
SICI code
0002-9939(1998)126:2<343:SSOGU>2.0.ZU;2-4
Abstract
Let G be an arbitrary group. If a epsilon ZG satisfies a(2) = 0, a not equal 0, then the units 1 + a, 1 + a generate a nonabelian free subg roup of units. As an application we show that if G is contained in an almost subnormal subgroup V of units in ZG then either V contains a no nabelian free subgroup or all finite subgroups of G are normal. This w as known before to be true for finite groups G only.