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On Groups Acting on Trees of Finite Extensions of Free Groups |
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PP: 111-116 |
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doi:10.18576/msl/070206
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Author(s) |
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R. M. S. Mahmood,
Mourad Oqla Massadeh,
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Abstract |
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| 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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