附註:Proceedings of a conference held from 5 August 2001 - 18 August 2001 in the Mathematical Institute of the University of Oxford - Intro.
Includes bibliographical references.
Cover -- Series-title -- Title -- Copyright -- Contents of Volume 1 -- Contents of Volume 2 -- INTRODUCTION -- PERMUTABILITY AND SUBNORMALITY IN FINITE GROUPS -- 1 Notation and terminology -- 2 Characterizations based on the normal structure -- 3 Characterizations based on the Sylow structure -- 4 Characterizations based on embedding properties -- References -- (PRO)-FINITE AND (TOPOLOGICALLY) LOCALLY FINITE GROUPS WITH A CC-SUBGROUP -- 1 Introduction -- 1.1 Sketching the thread -- 2 Announcement of the results -- References -- TABLE ALGEBRAS GENERATED BY ELEMENTS OF SMALL DEGREES.
1 Introduction -- 1.1 Examples -- 1.2 Wreath, tensor and fibred products -- 2 Classification results about standard integral table algebras -- 2.1 The algebras -- 2.2 The algebras -- 3 Normalized table algebras generated by a nonreal element of degree 3 -- References -- SUBGROUPS WHICH ARE A UNION OF A GIVEN NUMBER OF CONJUGACY CLASSES -- 1 Introduction -- 2 On n-decomposable finite groups -- References -- SOME RESULTS ON FINITE FACTORIZED GROUPS -- References -- ON NILPOTENT-LIKE FITTING FORMATIONS -- 1 Introduction -- 2 Lattice formations -- 3 Formations with the Shemetkov property.
4 Extensions of p-nilpotent groups -- 5 Dominant Fitting classes -- References -- LOCALLY FINITE GROUPS WITH MIN-p FOR ALL PRIMES p -- References -- QUASI-PERMUTATION REPRESENTATIONS OF 2-GROUPS OF CLASS 2 WITH CYCLIC CENTRE -- 1 Introduction -- 2 Calculating p(G), c(G) and q(G) -- 3 Quasi-permutation representations of an extraspecial 2-group -- References -- GROUPS ACTING ON BORDERED KLEIN SURFACES WITH MAXIMAL SYMMETRY -- 1 Introduction -- 2 Preliminaries -- 3 Properties of M-groups -- 4 Families of M-groups -- 5 Relations between Hurwitz, H, and M-groups -- References.
BREAKING POINTS IN SUBGROUP LATTICES -- 1 Introduction -- 2 The proof of the Theorem -- 3 Final remarks -- References -- GROUP ACTIONS ON GRAPHS, MAPS AND SURFACES WITH MAXIMUM SYMMETRY -- 1 Introduction -- 2 Methods for dealing with finitely-presented groups -- 2.1 Computational algorithms -- 2.2 Low index subgroups -- 2.3 Low index normal subgroups -- 2.4 Schreier coset graphs -- 3 Automorphism groups of compact Riemann surfaces -- 3.1 Hurwitz's theorem -- 3.2 Hurwitz groups -- 4 Regular maps -- 4.1 Definitions and background -- 4.2 Genus calculation.
4.3 Group theoretic construction of regular maps -- 4.4 Non-orientable regular maps -- 4.5 Regular maps of small genus -- 4.6 Group actions on non-orientable surfaces -- 5 Symmetric graphs -- 5.1 Definitions and background -- 5.2 The trivalent case -- 5.3 Finite 7-arc-transitive graphs -- 6 Some unexpected results/surprises -- 7 Some open problems -- Acknowledgement -- Electronic Availability -- References -- ON DUAL PRONORMAL SUBGROUPS AND FITTING CLASSES -- 1 Introduction -- 2 Relevant families of subgroups being F-dual pronormal -- 3 Local normality concepts between Fitting classes.
摘要:This first volume of the two-volume book contains selected papers from the international conference 'Groups St Andrews 2001 in Oxford' which was held at the University of Oxford in August 2001. Five main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions from Marston Conder (Auckland), Persi Diaconis (Stanford) and Marcus Du Sautoy (Cambridge). The series of Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the.
