UID:
almafu_9959239103902883
Format:
1 online resource (360 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88411-5
,
1-107-36613-5
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1-107-37086-8
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1-107-36122-2
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1-107-36948-7
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1-299-40393-X
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1-107-36367-5
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0-511-66188-6
Series Statement:
London Mathematical Society lecture note series ; 71
Content:
This book contains selected papers from the international conference 'Groups - St Andrews 1981', which was held at the University of St Andrews in July/August 1981. Its contents reflect the main topics of the conference: combinatorial group theory; infinite groups; general groups, finite or infinite; computational group theory. Four courses, each providing a five-lecture survey, given by J. Neubuser (Aachen), D. J. S. Robinson (Illinois), S. J. Tobin (Galway) and J. Wiengold (Cardiff), have been expanded into articles, forming the first part of the book. The second part consists of surveys and research articles written by other conference participants. More than two-thirds of the book is composed of survey articles providing a remarkably clear and up-to-date picture of those areas of group theory. The articles which comprise this book, together with their extensive bibliographies, will prove an invaluable tool to researchers in group theory, and, in addition, their detailed expositions make them very suitable for relevant postgraduate courses.
Note:
Proceedings of an international meeting held at the University of St. Andrews, July 25-Aug. 8, 1981.
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Cover; Title; Copyright; Contents; Preface; Twenty-five years of Groups St Andrews Conferences; ORIGINAL INTRODUCTION; 1. An elementary introduction to coset table methods in computational group theory; 0. PROLOGUE; 1. THE TODD-COXETER METHOD; 2. SOME ASPECTS FOR THE IMPLEMENTATION; 3. INFORMATION OBTAINABLE FROM A COSET TABLE; 4. FIRST VARIATION ON THE THEME OF TOW AND COXETER: PRESENTATIONS FOR A SUBGROUP; 5. SECOND VARIATION ON THE THEME OF TOW AND COXETER: PRESENTATIONS FOR A CONCRETE GROUP; 6. THIRD VARIATION ON THE THEME OF TOW AND COXETER: ALL SUBGROUPS OF LOW INDEX
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7. YET ANOTHER OCCURRENCE OF THE THEME OF TODD AND COXETER: A SIDE-GLANCE ON THE SCHREIER-TODD-COXETER-SIMS METHOD8. EPILOGUE; REFERENCES; 2. Applications of cohomology to the theory of groups; INTRODUCTION; CONTENTS; 1. CONJUGACY OF COMPLEMENTS AND THE FIRST COHOMOLOGY GROUP; 2. GROUP EXTENSIONS AND THE SECOND COHOMOLOGY GROW; 3. APPLICATIONS OF SPLITTING AND NEAR SPLITTING; I. Nilpotent supplements; II. Finitely generated soluble groups of finite rank; III. Nearly maximal subgroups; 4. AUTOMORPHISMS OF GROUP EXTENSIONS; 5. CONSTRUCTING OUTER AUTOMORPHISMS
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I. Automorphisms of free abelianized extensionsII. Outer automorphisms of finite p-groups; III. Comp lete groups; BIBLIOGRAPHY; 3. Groups with exponent four; INTRODUCTION; 1. BURNSIDE AND EXPONENT FOUR; A) Burnside groups; B) Commutators; C) Groups with exponent four: the Sanov theorem; D) Groups with exponent four: the Tobin theorem; 2. COMMUTATOR LAWS IN GROUPS WITH EXPONENT FOUR; A) Basic congruences; B) The group B(2); C) The groups B(n), n 〉 2; 3. COMMUTATOR STRUCTURE UNDER ADDITIONAL CONSTRAINTS; A) Commutator Conditions; B) Conditions on the Generators
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4. THE CLASS OF B(n) AND SOLVABILITY5. RECENT DEVELOPMENTS; REFERENCES; 4. The Schur multiplier: an elementary approach; 1. HISTORICAL INTRODUCTION AND APOLOGIA; 2. TRANSFER AND GROWS WITH FINITE CENTRAL FACTOR-GROUPS; 3. MULTIPLIERS VIA PRESENTATIONS AND DEFINING PAIRS; 4. SYLOW THEORY OF THE MULTIPLIER. SOME BETTER BOUNDS; 5. MULTIPLIERS OF DIRECT PRODUCTS. ABELIAN GROUPS. DEFICIENCY PR0BLEMS; 6. SOME HARDER PROBLEMS CONCERNED WITH MULTIPLIERS; REFERENCES; 5. A procedure for obtaining simplified defining relations for a subgroup; 1. INTRODUCTION; 2. THE MODIFIED ALGORITHM
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8. The maximal subgroups of the Chevalley group G2(4)
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English
Additional Edition:
ISBN 0-521-28974-2
Language:
English
URL:
https://doi.org/10.1017/CBO9780511661884
