scholarly journals Groups with one defining relator

1964 ◽  
Vol 4 (4) ◽  
pp. 385-392 ◽  
Author(s):  
Gilbert Baumslag
Keyword(s):  
Finite Number ◽  
Algebraic Theory ◽  
Late Nineteenth Century ◽  
Simple Type ◽  
Modern Theory ◽  
Infinite Groups ◽  
Finitely Presented Groups ◽  
Late Nineteenth ◽  
Finitely Presented ◽  
Finitely Related

The present day theory of finite groups might be regarded as the outgrowth of the algebraic theory of equations. In much the same way one might consider the modern theory of infinite groups as stemming from late nineteenth century topology. The groups that crop up in topology are of a particularly simple type in that they are both finitely generated and finitely related. This means that every element in such a group can be expressed in terms of a finite number of elements and their inverses and every relation is an algebraic consequence of a finite number of relations between these elements. In other words the legacy of topology to group theory is the estate of finitely presented groups. This talk is concerned with the seemingly simplest of the finitely presented groups, the so-called groups with a single defining relator.

Reflections on some aspects of infinite groups

2014 ◽  
Vol 6 (2) ◽  
Author(s):  
Benjamin Fine ◽  
Anthony Gaglione ◽  
Gerhard Rosenberger ◽  
Dennis Spellman
Keyword(s):  
Finitely Generated ◽  
Infinite Groups ◽  
Limit Groups ◽  
Finitely Presented Groups ◽  
The Relationship ◽  
Finitely Presented

AbstractIn this paper we survey and reflect upon several aspects of the theory of infinite finitely generated and finitely presented groups that were originally motivated by work of Gilbert Baumslag. All but the last of the topics we have chosen are all related in one way or another to the theory of limit groups and the solution of the Tarski problems. These include the residually free and fully residually free properties and the big powers condition; Baumslag doubles and extensions of centralizers; residually-𝒳 groups and extensions of results of Benjamin Baumslag and finally the relationship between CT and CSA groups.

scholarly journals A three-player coherent state embezzlement game

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 349
Author(s):  
Zhengfeng Ji ◽  
Debbie Leung ◽  
Thomas Vidick
Keyword(s):  
Representation Theory ◽  
Coherent State ◽  
Finite Number ◽  
Success Probability ◽  
High Dimensional ◽  
Entangled States ◽  
Entangled State ◽  
Finitely Presented Groups ◽  
Questions And Answers ◽  
Finitely Presented

We introduce a three-player nonlocal game, with a finite number of classical questions and answers, such that the optimal success probability of 1 in the game can only be achieved in the limit of strategies using arbitrarily high-dimensional entangled states. Precisely, there exists a constant 0<c≤1 such that to succeed with probability 1−ε in the game it is necessary to use an entangled state of at least Ω(ε−c) qubits, and it is sufficient to use a state of at most O(ε−1) qubits. The game is based on the coherent state exchange game of Leung et al.\ (CJTCS 2013). In our game, the task of the quantum verifier is delegated to a third player by a classical referee. Our results complement those of Slofstra (arXiv:1703.08618) and Dykema et al.\ (arXiv:1709.05032), who obtained two-player games with similar (though quantitatively weaker) properties based on the representation theory of finitely presented groups and C∗-algebras respectively.

Contents of Western Sociology of Religion as a Science and Educational Discipline

2002 ◽  
pp. 106-110
Author(s):  
Liudmyla O. Fylypovych
Keyword(s):  
Nineteenth Century ◽  
International Society ◽  
Sociology Of Religion ◽  
Scientific Study ◽  
Late Nineteenth Century ◽  
The West ◽  
Late Nineteenth

Sociology of religion in the West is a field of knowledge with at least 100 years of history. As a science and as a discipline, the sociology of religion has been developing in most Western universities since the late nineteenth century, having established traditions, forming well-known schools, areas related to the names of famous scholars. The total number of researchers of religion abroad has never been counted, but there are more than a thousand different centers, universities, colleges where religion is taught and studied. If we assume that each of them has an average of 10 religious scholars, theologians, then the army of scholars of religion is amazing. Most of them are united in representative associations of researchers of religion, which have a clear sociological color. Among them are the most famous International Society for the Sociology of Religion (ISSR) and the Society for Scientific Study of Religion (SSSR).

John Lloyd Williams (1854–1945): profile of a Snowdonian botanist

2006 ◽  
Vol 33 (1) ◽  
pp. 1-17
Author(s):  
Dewi Jones
Keyword(s):  
Nineteenth Century ◽  
Plant Physiology ◽  
Marine Algae ◽  
Plant Distribution ◽  
The Arctic ◽  
Late Nineteenth Century ◽  
Major Study ◽  
The Subject ◽  
Late Nineteenth

John Lloyd Williams was an authority on the arctic-alpine flora of Snowdonia during the late nineteenth century when plant collecting was at its height, but unlike other botanists and plant collectors he did not fully pursue the fashionable trend of forming a complete herbarium. His diligent plant-hunting in a comparatively little explored part of Snowdonia led to his discovering a new site for the rare Killarney fern (Trichomanes speciosum), a feat which was considered a major achievement at the time. For most part of the nineteenth century plant distribution, classification and forming herbaria, had been paramount in the learning of botany in Britain resulting in little attention being made to other aspects of the subject. However, towards the end of the century many botanists turned their attention to studying plant physiology, a subject which had advanced significantly in German laboratories. Rivalry between botanists working on similar projects became inevitable in the race to be first in print as Lloyd Williams soon realized when undertaking his major study on the cytology of marine algae.

Illustrated Media, the Built Environment and Identity Politics in Fin-de-siècle Catalonia: Printing Images, Making the Nation

2015 ◽  
Vol 4 (2) ◽  
pp. 113-135
Author(s):  
Lucila Mallart
Keyword(s):  
Nineteenth Century ◽  
Built Environment ◽  
Identity Politics ◽  
Nation Building ◽  
Constitutive Relationship ◽  
Fin De Siecle ◽  
Late Nineteenth Century ◽  
Fin De Siècle ◽  
Late Nineteenth

This article explores the role of visuality in the identity politics of fin-de-siècle Catalonia. It engages with the recent reevaluation of the visual, both as a source for the history of modern nation-building, and as a constitutive element in the emergence of civic identities in the liberal urban environment. In doing so, it offers a reading of the mutually constitutive relationship of the built environment and the print media in late-nineteenth century Catalonia, and explores the role of this relation as the mechanism by which the so-called ‘imagined communities’ come to exist. Engaging with debates on urban planning and educational policies, it challenges established views on the interplay between tradition and modernity in modern nation-building, and reveals long-term connections between late-nineteenth-century imaginaries and early-twentieth-century beliefs and practices.

Translating the Scribe: Lithographic Print and Vernacularization in Colonial India, 1857–1915

2019 ◽  
Vol 16 (2-3) ◽  
pp. 281-300
Author(s):  
Amanda Lanzillo
Keyword(s):  
Nineteenth Century ◽  
South Asia ◽  
Indian Subcontinent ◽  
North India ◽  
Late Nineteenth Century ◽  
Book Production ◽  
Manuscript Culture ◽  
Arabic Script ◽  
Literary Cultures ◽  
Late Nineteenth

Focusing on the lithographic print revolution in North India, this article analyses the role played by scribes working in Perso-Arabic script in the consolidation of late nineteenth-century vernacular literary cultures. In South Asia, the rise of lithographic printing for Perso-Arabic script languages and the slow shift from classical Persian to vernacular Urdu as a literary register took place roughly contemporaneously. This article interrogates the positionality of scribes within these transitions. Because print in North India relied on lithography, not movable type, scribes remained an important part of book production on the Indian subcontinent through the early twentieth century. It analyses the education and models of employment of late nineteenth-century scribes. New scribal classes emerged during the transition to print and vernacular literary culture, in part due to the intervention of lithographic publishers into scribal education. The patronage of Urdu-language scribal manuals by lithographic printers reveals that scribal education in Urdu was directly informed by the demands of the print economy. Ultimately, using an analysis of scribal manuals, the article contributes to our knowledge of the social positioning of book producers in South Asia and demonstrates the vitality of certain practices associated with manuscript culture in the era of print.

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