Presentation of groups acting on trees with inversions
01 Jan 1989-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (Cambridge University Press)-Vol. 113, pp 235-241
About: This article is published in Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences.The article was published on 1989-01-01. It has received 15 citations till now.
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01 Aug 2019
TL;DR: In this paper, the authors analyze on public perception about policy change toward the new learner's acceptance policy (PPDB) 2019 in Surakarta Public senior high schools.
Abstract: By the year in 2017 the implementation of new learner’s acceptance policy (PPDB) in Surakarta Public senior high schools had been changed. In 2017 the policy emphasized with its social accessible one by receiving quota till 20%. however, in 2018 when the policy still being implemented there were changes thus added the zoning system. Ministry of Education and Culture said in 2019 they will enforce the zoning policy and the Poor Certificate of Unable will no longer to be main requirement. Since 2017 Surakarta State Senior High Schools PPDB experienced a lot of polemic and it became public concern. Polemics that occurred from the last two years illustrates there are many people who have different perceptions toward this policy; meaning that although the policy is not necessarily understood by the public yet many differences in interpreting had been occurred. So, this study will analyze on public perception about policy change toward the PPDB 2019 in Surakarta. The research will use qualitative method. Keywords—perception; public policy; policy evaluation
6 citations
Cites background from "Presentation of groups acting on tr..."
...Terbentuknya object on the environment based on the stimulus or situation at hand Related condition assessment process the public perception is a person or group of people to an object, event with involving experiences associated with these objects through the process of cognition, affect, and konasi to form the object [25]....
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TL;DR: In this article, the subgroup theorem for groups acting on======trees with inversions was extended to quasi-HNN groups, and the main technique used is the sub-group theorem.
Abstract: We extend the structure theorem for the subgroups of the class of
HNN groups to a new class of groups called quasi-HNN groups. The
main technique used is the subgroup theorem for groups acting on
trees with inversions.
4 citations
Cites background from "Presentation of groups acting on tr..."
...For definitions of subgraphs, trees, morphisms of graphs, and Aut(X), the set of all automorphisms of the graph X which is a group under the composition of morphisms of graphs, see [5] or [9]....
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...In this section, we summarize the presentation for groups of groups acting on trees with inversions obtained by [5]....
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TL;DR: In this article, it was shown that if G is a group acting on a tree X with inversions such that G does not fix any element of X, then an element g of G is invertor if and only if g is not in any vertex stabilizer of G and g 2 is in an edge stabilizer.
Abstract: An element of a group acting on a graph is called invertor if it transfers an edge of the graph to its inverse. In this paper, we show that if G is a group acting on a tree X with inversions such that G does not fix any element of X, then an element g of G is invertor if and only if g is not in any vertex stabilizer of G and g 2 is in an edge stabilizer of G. Moreover, if H is a finitely generated subgroup of G, then H contains an invertor element or some conjugate of H contains a cyclically reduced element of length at least one on which H is not in any vertex stabilizer of G ,o rH is in a vertex stabilizer of G.
2 citations
TL;DR: In this article, it was shown that if a group acting on a graph X with inversions has a presentation induced by a fundamental domain for the action of G on X, then X is a tree.
Abstract: In this paper we show that if G is a group acting on a graph X with inversions such that G has a presentation induced by a fundamental domain for the action of G on X, then X is a tree.
2 citations
14 Jul 2021
TL;DR: In this article, it was shown that if H and G are two groups and p: H→G is an epimorphism such that G is a quasi-treed HNN group, then H is a treed HNN.
Abstract: We say that a group G acts on a graph X with inversions if there exist an element g∈G and an edge e∈X such that g transfers e to its inverse $\bar e$, that is, $g\left(e\right) = \bar e$. A group is called a quasi-treed HNN (treed HNN) group if there exists a tree on which the group acts on with inversion (without inversions) and fixing no elements of the tree. The aim of the paper is to prove that if H and G are two groups and p: H→G is an epimorphism such that G is a quasi-treed HNN group (treed HNN), then H is a quasi-treed HNN group (treed HNN). As an application, we show that if N is a normal subgroup of the group G such that the quotient group G/N is a quasi-treed HNN group (or is a treed HNN group), then H is a quasi-treed HNN group (or is a treed HNN group).
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