On fibers and accessibility of groups acting on trees with inversions
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...
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| Дата: | 2015 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2015
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154252 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
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irk-123456789-1542522019-06-16T01:27:02Z On fibers and accessibility of groups acting on trees with inversions Mahmood, R.M.S. 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. 2015 Article 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 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Mahmood, R.M.S. |
| spellingShingle |
Mahmood, R.M.S. On fibers and accessibility of groups acting on trees with inversions Algebra and Discrete Mathematics |
| author_facet |
Mahmood, R.M.S. |
| author_sort |
Mahmood, R.M.S. |
| title |
On fibers and accessibility of groups acting on trees with inversions |
| title_short |
On fibers and accessibility of groups acting on trees with inversions |
| title_full |
On fibers and accessibility of groups acting on trees with inversions |
| title_fullStr |
On fibers and accessibility of groups acting on trees with inversions |
| title_full_unstemmed |
On fibers and accessibility of groups acting on trees with inversions |
| title_sort |
on fibers and accessibility of groups acting on trees with inversions |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154252 |
| citation_txt |
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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT mahmoodrms onfibersandaccessibilityofgroupsactingontreeswithinversions |
| first_indexed |
2023-05-20T17:43:31Z |
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2023-05-20T17:43:31Z |
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1796153945174835200 |