On fibers and accessibility of groups acting on trees with inversions
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On fibers and accessibility of groups acting on trees with inversions
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| Creator |
Mahmood, R.M.S.
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| Description |
Throughout this paper the actions of groups on graphs with inversions are allowed. An element g of a group G is called inverter if there exists a tree X where G acts such that g transfers an edge of X into its inverse. A group G is called accessible if G is finitely generated and there exists a tree on which G acts such that each edge group is finite, no vertex is stabilized by G, and each vertex group has at most one end. In this paper we show that if G is a group acting on a tree X such that if for each vertex v of X, the vertex group Gv of v acts on a tree Xv, the edge group Ge of each edge e of X is finite and contains no inverter elements of the vertex group Gt(e) of the terminal t(e) of e, then we obtain a new tree denoted Xe and is called a fiber tree such that G acts on Xe. As an application, we show that if G is a group acting on a tree X such that the edge group Ge for each edge e of X is finite and contains no inverter elements of Gt(e), the vertex Gv group of each vertex v of X is accessible, and the quotient graph G /X for the action of G on X is finite, then G is an accessible group. |
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| Date |
2019-06-15T11:49:19Z
2019-06-15T11:49:19Z 2015 |
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| Type |
Article
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| Identifier |
On fibers and accessibility of groups acting on trees with inversions / R.M.S. Mahmood // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 229-242. — Бібліогр.: 11 назв. — англ.
1726-3255 2000 MSC:20E06, 20E086, 20F05 http://dspace.nbuv.gov.ua/handle/123456789/154252 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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