scholarly journals Algebraic characterisation of relatively hyperbolic special groups

2021 ◽  
Vol 241 (1) ◽  
pp. 301-341
Author(s):  
Anthony Genevois
Author(s):  
Maulana Akbar Shah @ U Tun Aung

Abstract In addition to compliance with the five pillars of Islam, Da’wah Islamiyyah is an indispensable act for Muslims who view their life missions as to propagate Islam. The act of da’wah is a mission only undertaken by those who are selected to do so, as Allah SWT said: “You are the best of peoples, taken out for mankind, you enjoin what is right, forbid what is wrong…,” (Al-Qur’an, Al- `Imran, 3:110). The phrase “you are taken out for mankind” is a very clear phrase which refers to a special group. Many du’at propagate Islam through regular procedures. In this contemporary day and age, it would be more successful if creative da’wah methodologies are used to special groups where special talent is required. Examples of these special target groups are individuals such as [1] pregnant mothers, [2] mothers of new born babies, [3] parents of toddlers, [4] parents of children [5] youth, teenagers and adolescents, [6] married couples, [7] elderly or aged individuals and [8] non-Muslims.  They are good targets to promote Islam. Thus, du’at must have special talents and knowledge to do so. In this regard, du’at must be equipped with exceptional knowledge of the target groups to propagate Islam effectively. The present paper attempts to highlight the distinctive natures of the above mentioned categories of individuals and explores how du’at should approach them when he or she encounters them for the purpose of promoting Islam.        Keywords: Call to Islam, Da’wah Islamiyyah, creative da’wah, creative da’ie, enjoin good, forbid evil.   Abstrak Selain mematuhi 5 rukun Islam, dakwah Islamiyyah tidak dapat diasingkan daripada seseorang Muslim yang bermatlamat untuk menyebarkan ajaran Islam. Berdakwah adalah suatu tugas yang hanya dijalankan oleh mereka yang terpilih. Seperti yang diwahyukan oleh Allah SWT “Kamu adalah sebaik-baik umat yang dilahirkan bagi umat manusia, kerana kamu menyuruh berbuat segala perkara yang baik dan melarang daripada segala perkara yang buruk dan keji...” (Al-Quran, Al-Imran, 3:110). Frasa “umat yang dilahirkan bagi umat manusia”  jelas dinyatakan di mana ia merujuk kepada satu golongan yang istimewa. Kebanyakan pendakwah menyebarkan Islam melalui metodologi yang sudah menjadi kebiasaan. Bagaimanapun, pada zaman ini, pendakwahan akan lebih berjaya jika kaedah yang kreatif digunakan kepada beberapa golongan yang tertentu. Antara contoh golongan yang dimaksudkan adalah [1] wanita yang mengandung, [2] ibu kepada bayi yang baru lahir, [3] ibu bapa kepada anak-anak kecil, [4] ibu bapa kepada kanak-kanak, [5] golongan belia dan remaja, [6] pasangan suami isteri, [7] warga emas, dan [8] golongan bukan Islam. Mereka merupakan sasaran yang sempurna untuk mempelajari Islam. Oleh hal demikian, para pendakwah mesti mempunyai bakat yang istimewa dan ilmu yang mencukupi untuk berdakwah. Para pendakwah juga harus memahami kumpulan sasaran dengan menyeluruh supaya penyebaran ajaran Islam akan lebih berkesan. Tujuan penulisan ini adalah untuk menggariskan sifat unik golongan yang dinyatakan di atas dan menerokai bagaimana para pendakwah harus mendekati mereka dengan niat untuk menyebarkan Islam.   Kata Kunci: Panggilan kepada Islam, dakwah Islamiyyah, dakwah kreatif, da’ie kreatif, menyuruh kepada kebaikan, menghalang daripada kejahatan.  


Author(s):  
Jacob Russell ◽  
Davide Spriano ◽  
Hung Cong Tran

AbstractWe show the mapping class group, $${{\,\mathrm{CAT}\,}}(0)$$ CAT ( 0 ) groups, the fundamental groups of closed 3-manifolds, and certain relatively hyperbolic groups have a local-to-global property for Morse quasi-geodesics. This allows us to generalize combination theorems of Gitik for quasiconvex subgroups of hyperbolic groups to the stable subgroups of these groups. In the case of the mapping class group, this gives combination theorems for convex cocompact subgroups. We show a number of additional consequences of this local-to-global property, including a Cartan–Hadamard type theorem for detecting hyperbolicity locally and discreteness of translation length of conjugacy classes of Morse elements with a fixed gauge. To prove the relatively hyperbolic case, we develop a theory of deep points for local quasi-geodesics in relatively hyperbolic spaces, extending work of Hruska.


1998 ◽  
Vol 10 (2) ◽  
pp. 134-135 ◽  
Author(s):  
ELENA GARRALDA
Keyword(s):  

2002 ◽  
Vol 11 (1) ◽  
pp. 21-34 ◽  
Author(s):  
LESLIE ANN GOLDBERG ◽  
MARK JERRUM

We consider the problem of sampling ‘unlabelled structures’, i.e., sampling combinatorial structures modulo a group of symmetries. The main tool which has been used for this sampling problem is Burnside’s lemma. In situations where a significant proportion of the structures have no nontrivial symmetries, it is already fairly well understood how to apply this tool. More generally, it is possible to obtain nearly uniform samples by simulating a Markov chain that we call the Burnside process: this is a random walk on a bipartite graph which essentially implements Burnside’s lemma. For this approach to be feasible, the Markov chain ought to be ‘rapidly mixing’, i.e., converge rapidly to equilibrium. The Burnside process was known to be rapidly mixing for some special groups, and it has even been implemented in some computational group theory algorithms. In this paper, we show that the Burnside process is not rapidly mixing in general. In particular, we construct an infinite family of permutation groups for which we show that the mixing time is exponential in the degree of the group.


2015 ◽  
Vol 9 (2) ◽  
pp. 599-663 ◽  
Author(s):  
Vincent Guirardel ◽  
Gilbert Levitt

2018 ◽  
Vol 79 (9) ◽  
pp. 1609-1620 ◽  
Author(s):  
D. V. Efanov ◽  
V. V. Sapozhnikov ◽  
Vl. V. Sapozhnikov
Keyword(s):  

1992 ◽  
Vol 16 (6) ◽  
pp. 336-337
Author(s):  
R. S. Augustine ◽  
P. N. Kurian ◽  
A. Michael

This audit examined 65 consecutive admissions to a psychiatric hospital in the Irish Midlands over six months. The admissions came from a defined sector with a total population of 39,000. In the year prior to the study major changes in the delivery of psychiatric care in the sector were instituted. These changes included the introduction of admission guidelines and extra resources in the community. The general practitioners who see mental illness at first contact were informed of these changes. Attempts were made by the sector psychiatrist team to screen for appropriateness of admission with regard to the special groups such as alcoholics, the aged and the mentally handicapped.


Author(s):  
Anthony Genevois

In this paper, we initiate a geometric study of graph braid groups. More precisely, by applying the formalism of special colorings introduced in a previous paper, we determine precisely when a graph braid group is Gromov-hyperbolic, toral relatively hyperbolic and acylindrically hyperbolic.


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