FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 7, PAGES 15-21

The ranks of central unit groups of integral group rings of alternating groups

R. Zh. Aleev
A. V. Kargapolov
V. V. Sokolov

Abstract

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Let $G$ be a finite group and $U(Z($ZG)) be the group of units of the center $Z($ZG) of the integral group ring $$ZG (the central unit group of the ring $$ZG). The purpose of the present work is to study the ranks $r$_n of groups $U(Z($ZA_n)), i.e., of central unit groups of integral group rings of alternating groups $A$_n. We shall find all values $n$ for $r$_n = 1 and propose an approach how to describe the groups $U(Z($ZA_n)) in these cases, and we will present some results of calculations of $r$_n for $n$£ 600.

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Last modified: June 25, 2009