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 $U(Z($**Z**G)) be the group
of units of the center $Z($**Z**G)
of the integral group ring $$**Z**G (the
central unit group of the ring $$**Z**G).
The purpose of the present work is to study the ranks $r$_{n} of groups
$U(Z($**Z**A_{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 $U(Z($**Z**A_{n}))
in these cases, and we will present
some results of calculations of $r$_{n} for
$n$£
600.

Location: http://mech.math.msu.su/~fpm/eng/k08/k087/k08702h.htm

Last modified: June 25, 2009