International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 20, Pages 1241-1249
On centralizers of elements of groups acting on trees with
College of Education and Basic Science, Ajman University of Science and Technology, Abu Dhabi, United Arab Emirates
Received 2 May 2002
Copyright © 2003 R. M. S. Mahmood. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A subgroup of a group is called malnormal in if it satisfies the condition that if and ,
such that , then . In this paper, we show
that if is a group acting on a tree with inversions such
that each edge stabilizer is malnormal in , then the
centralizer of each nontrivial element of is in a
vertex stabilizer if is in that vertex stabilizer. If is
not in any vertex stabilizer, then is an infinite cyclic
if does not transfer an edge of to its inverse. Otherwise,
is a finite cyclic of order 2.