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On the Normalizer Problem

✍ Scribed by E. Jespers; S.O. Juriaans; J.M. de Miranda; J.R. Rogerio

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 117 KB
Volume: 247
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8724

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✦ Synopsis

In this paper the normalizer problem of an integral group ring of an arbitrary group G is investigated. It is shown that any element of the normalizer 1 G of G in the group of normalized units 1 G is determined by a finite normal subgroup. This reduction to finite normal subgroups implies that the normalizer property holds for many classes of (infinite) groups, such as groups without non-trivial 2-torsion, torsion groups with a normal Sylow 2-subgroup, and locally nilpotent groups. Further it is shown that the commutator of 1 G equals G and 1 G /G is finitely generated if the torsion subgroup of the finite conjugacy group of G is finite.

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