Presentations for subsemigroups of groups

This thesis studies subsemigroups of groups from three perspectives: automatic structures, ordinary semigroup presentations, and Malcev presentaions. [A Malcev presentation is a presentation of a special type for a semigroup that can be embedded into a group. A group-embeddable semigroup is Malcev coherent if all of its finitely generated subsemigroups admit finite Malcev presentations.] The theory of synchronous and asynchronous automatic structures for semigroups is expounded, particularly for group-embeddable semigroups. In particular, automatic semigroups embeddable into groups are shown to inherit many of the pleasant geometric properties of automatic groups. It is proved that group- embeddable automatic semigroups admit finite Malcev presentations, and such presentations can be found effectively. An algorithm is exhibited to test whether an automatic semigroup is a free semigroup. Cancellativity of automatic semigroups is proved to be undecidable. Study is made of several classes of groups: virtually free groups; groups that satisfy semigroup laws (in particular [virtually] nilpotent and [virtually] abelian groups); polycyclic groups; free and direct products of certain groups; and one-relator groups. For each of these classes, the question of Malcev coherence is considered, together with the problems of whether finitely generated subsemigroups are finitely presented or automatic. This study yields closure and containment results regarding the class of Malcev coherent groups. The property of having a finite Malcev presentation is shown to be preserved under finite Rees index extensions and subsemigroups. Other concepts of index are also studied

Rebirth, reform, and resilience: universities in transition, 1300-1700

(print) 367 p., [1] p. of plates ; 24 cmUniversities in transition, 1300-1700JAMES M. KITTELSON : OHIO STATE UNIVERSITY Introduction : The Durability of the Universities of Old Europe 1 -- HEIKO A. OBERMAN : UNIVERSITY OF TUBINGEN University and Society on the Threshold of Modern Times : The German Connection 19 -- LEWIS W. SPITZ : STANFORD UNIVERSITY The Importance of the Reformation for Universities : Culture and Confession in the Critical Years 42 -- EDWARD GRANT : INDIANA UNIVERSITY Science and the Medieval University 68 -- WILLIAM J. COURTENAY : UNIVERSITY OF WISCONSIN The Role of English Thought in the Transformation of University Education in the Late Middle Ages 103 -- JOHN M. FLETCHER : UNIVERSITY OF ASTON IN BIRMINGHAM University Migrations in the Late Middle Ages with Particular Reference to the Stamford Secession 163 -- PAUL W. KNOLL : UNIVERSITY OF SOUTHERN CALIFORNIA The University of Cracow in the Conciliar Movement 190 -- GUY FITCH LYTLE : UNIVERSITY OF TEXAS The Careers of Oxford Students in the Later Middle Ages 213 -- JAMES H. OVERFIELD : UNIVERSITY OF VERMONT University Studies and the Clergy in Pre-Reformation Germany 254 -- M. A. SCREECH : UNIVERSITY COLLEGE, LONDON Two Attitudes toward Hebrew Studies : Erasmus and Rabelais 293 -- JOHN M. FLETCHER and JULIAN DEAHL : UNIVERSITY OF ASTON IN BIRMINGHAM European Universities, 1300-1700 : The Development of Research, 1969-1979, with a Summary Bibliography 324 -- Notes on Contributors 359 -- Index 36