Open AccessHypercentral units in integral group rings
Author(s) -
Yuanlin Li,
M. M. Parmenter
Publication year - 2001
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-01-05848-8
Subject(s) - algorithm , artificial intelligence , annotation , computer science
In this note, we show that when G G is a torsion group the second center of the group of units U ( Z G ) U({\mathbb Z}G) of the integral group ring Z G {\mathbb Z}G is generated by its torsion subgroup and by the center of U ( Z G ) U({\mathbb Z}G) . This extends a result of Arora and Passi (1993) from finite groups to torsion groups, and completes the characterization of hypercentral units in Z G {\mathbb Z}G when G G is a torsion group.