International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 929871 | https://doi.org/10.1155/S0161171203205305

R. M. S. Mahmood, "On centralizers of elements of groups acting on trees with inversions", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 929871, 9 pages, 2003. https://doi.org/10.1155/S0161171203205305

On centralizers of elements of groups acting on trees with inversions

Received02 May 2002

Abstract

A subgroup H of a group G is called malnormal in G if it satisfies the condition that if gG and hH, h1 such that ghg1H, then gH. In this paper, we show that if G is a group acting on a tree X with inversions such that each edge stabilizer is malnormal in G, then the centralizer C(g) of each nontrivial element g of G is in a vertex stabilizer if g is in that vertex stabilizer. If g is not in any vertex stabilizer, then C(g) is an infinite cyclic if g does not transfer an edge of X to its inverse. Otherwise, C(g) is a finite cyclic of order 2.

Copyright © 2003 Hindawi Publishing Corporation. 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.


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