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
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.
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