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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 7 > No. 2


On Groups Acting on Trees of Finite Extensions of Free Groups

PP: 111-116
R. M. S. Mahmood, Mourad Oqla Massadeh,
A group G has the property P if G is finitely generated and is of a finite extension of a free group. In this paper we prove that if the group G has the property P and H is a subgroup of G thenIf H is of finite index, then H has the property P or H is finite and normal, then the quotient group G/H has the property P. Furthermore, we prove that if G is a group acting on a tree X without inversions such that the stabilize Gv of each vertex v of X has the property P, Gv G, the stabilizer Ge of each edge e of X is finite, and the quotient graph G/X for the action of G on X is finite, then G has the property P. We have applications to tree product of the groups and HNN extension groups.

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