Glasgow Mathematical Journal

Table of Contents - January 2012 - Volume 54, Issue 01  

Research Article

DERIVED SUBGROUPS OF FIXED POINTS IN PROFINITE GROUPS

CRISTINA ACCIARRIa1, ALINE DE SOUZA LIMAa2 and PAVEL SHUMYATSKYa3

a1 Via Francesco Crispi, n.81 San Benedetto del Tronto (AP) Italy e-mail: acciarricristina@yahoo.it

a2 Department of Mathematics and Statistics, Federal University of Goiás, Goiânia-GO, 74001-970, Brazil e-mail: alinelima@mat.unb.br

a3 Department of Mathematics, University of Brasilia, Brasilia-DF 70910-900, Brazil e-mail: pavel@unb.br

Abstract

The main result of this paper is the following theorem. Let q be a prime and A be an elementary abelian group of order q3. Suppose that A acts as a coprime group of automorphisms on a profinite group G in such a manner that CG(a)′ is periodic for each a ∈ A#. Then G′ is locally finite.

(Received December 03 2010)

(Accepted April 28 2011)

(Online publication August 02 2011)

2010 Mathematics Subject Classification

  • 20E18;
  • 20D45;
  • 20F40