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 finite...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2015 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2015
|
| Онлайн доступ: | https://nasplib.isofts.kiev.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862745823061737472 |
|---|---|
| author | Mahmood, R.M.S. |
| author_facet | Mahmood, R.M.S. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T20:43:01Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154252 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T20:43:01Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Mahmood, R.M.S. 2019-06-15T11:49:19Z 2019-06-15T11:49:19Z 2015 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 https://nasplib.isofts.kiev.ua/handle/123456789/154252 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. The author would like to thank the referee for his(her) help and suggestions to improve the first draft of this paper. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On fibers and accessibility of groups acting on trees with inversions Article published earlier |
| spellingShingle | On fibers and accessibility of groups acting on trees with inversions Mahmood, R.M.S. |
| title | 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_short | On fibers and accessibility of groups acting on trees with inversions |
| title_sort | on fibers and accessibility of groups acting on trees with inversions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154252 |
| work_keys_str_mv | AT mahmoodrms onfibersandaccessibilityofgroupsactingontreeswithinversions |