Proceedings of the Second International Conference on the Theory of Groups : Australian National University, August 13-24, 1973

Front Matter....Pages I-VII Introduction....Pages 1-7 Periodic Groups of Odd Exponent....Pages 8-12 Einbettungseigenschaften von Normalteilern: Der Schluss vom Endlichen Aufs Unendliche....Pages 13-62 Characterisation of the Groups with the Gaschütz Cohomology Property....Pages 63-64 Finitely Presented Metabelian Groups....Pages 65-74 Some Problems on One-Relator Groups....Pages 75-81 Computation in Nilpotent Groups (Application)....Pages 82-89 Between Logic and Group Theory....Pages 90-102 On the Structure of Blocks of Characters of Finite Groups....Pages 103-130 Transitivity-Systems of Certain One-Relator Groups....Pages 131-140 Characteristic Subgroups of Free Groups....Pages 141-149 Metabelian Varieties of Groups....Pages 150-157 Subdirect Product Closed Fitting Classes....Pages 158-164 On the Rank of the Intersection of Subgroups of a Fuchsian Group....Pages 165-187 Subgroups of Binary Relations....Pages 188-196 The 2-Adic Representations of Klein’s Four Group....Pages 197-203 A General Purpose Group Theory Program....Pages 204-217 On the Modular Representations of the General Linear and Symmetric Groups....Pages 218-220 Words Which Give Rise to Another Group Operation for a Given Group....Pages 221-225 Classes of Finite Soluble Groups....Pages 226-237 A Note on Blocks....Pages 238-240 The Subgroup Theorem for Amalgamated Free Products, HNN-Constructions and Colimits....Pages 241-280 Linear Representations Over Principal Ideal Domains....Pages 281-284 A Property Common to the Weyl and Orthogonal Groups....Pages 285-287 Primitive Extensions of Maximal Diameter of Multiply Transitive Permutation Groups....Pages 288-297 Some Characters of Orthogonal Groups Over the Field of Two Elements....Pages 298-314 Type Sets and Admissible Multiplications....Pages 315-317 Power Series and Matrix Representations of Certain Relatively Free Groups....Pages 318-329 The Nilpotency Class of Finitely Generated Groups of Exponent Four....Pages 330-332 Hypocritical and Sincere Groups....Pages 333-336 Sylow Subgroups of Locally Finite Groups....Pages 337-346 A Reidemeister-Schreier Program....Pages 347-356 Non-Nilpotent Groups with Normalizer Condition....Pages 357-360 The Influence of 2-Sylow Intersections on the Structure of Finite Simple Groups....Pages 361-365 Rank Four Configurations....Pages 366-366 Some Nonsimplicity Criteria for Finite Groups....Pages 367-376 Free Subgroups of Free Topological Groups....Pages 377-387 Some Questions in the Theory of Soluble Groups....Pages 389-394 Locally Finite Simple Groups....Pages 395-400 Normal Subgroups of Groups of Prime-Power Order....Pages 401-408 Some Related Questions in the Theory of Groups and Lie Algebras....Pages 409-416 Hanna Neumann’s Problems on Varieties of Groups....Pages 417-431 Finite Projective Planes and Sharply 2-Transitive Subsets of Finite Groups....Pages 432-436 Non Euclidean Crystallographic Groups....Pages 437-442 On Subnormality in Soluble Minimax Groups....Pages 443-445 Varieties Generated by Finite Algebras....Pages 446-447 Computing with Finite Simple Groups....Pages 448-452 Compact Torsion Groups....Pages 453-462 Braid Groups: A Survey....Pages 463-487 Two-Bridge Knots have Residually Finite Groups....Pages 488-493 Periodic Automorphisms of the Two-Generator Free Group....Pages 494-498 On Groups of Exponent Four: A Criterion for Nonsolvability....Pages 499-503 The Topology of Free Products of Topological Groups....Pages 504-515 Some Groups I have Known....Pages 516-519 Transitive Permutation Groups of Prime Degree....Pages 520-535 Ideals in the Centre of a Group Ring....Pages 536-540 A Non-Distributive Metabelian Variety Lattice....Pages 541-549 Polynomial Maps....Pages 550-561 Über Erzeugende Ebener Diskontinuierlicher Gruppen....Pages 562-564 Contribution to the Theory of Abstract Groups....Pages 565-577 Sylow Subgroups of Finite Permutation Groups....Pages 578-579 On the Nielsen Equivalence of Pairs of Generators in Certain HNN Groups....Pages 580-588 The Collineation Groups of Finite Generalized Hall Planes....Pages 589-594 Abelian Groups with Self-Injective Endomorphism Rings....Pages 595-604 Lattice Isomorphisms and Saturated Formations of Finite Soluble Groups....Pages 605-610 Some Reflections on HNN Extensions....Pages 611-632 Amalgames et Points Fixes....Pages 633-640 Geometric Characterizations in Finite Group Theory....Pages 641-654 Torsion-Free Metabelian Groups with Infinite Cyclic Quotient Groups....Pages 655-666 On the Lie Ring of a Group of Prime Exponent....Pages 667-690 Computation in Nilpotent Groups (Theory)....Pages 691-700 On Groups Admitting an Elementary Abelian Automorphism Group....Pages 701-704 Varieties Described by Verbal Subgroups....Pages 705-708 A Relation in Free Products....Pages 709-716 A Note on Subsoluble Groups....Pages 717-718 On Generalized Soluble Groups....Pages 719-729 Finite Groups with Sylow 2-Subgroups of Type the Alternating Group of Degree Sixteen....Pages 730-732 Problem Section....Pages 733-740 Back Matter....Pages 743-744 Annotation This volume consists of papers presented to the Second International Conference on the Theory of Groups held in Canberra in August 1973 together with areport by the chairman of the Organizing Committee and a collection of problems. The manuscripts were typed by Mrs Geary, the bulk of the bibliographie work was done by Mrs Pinkerton, and a number of colleagues helped with proof-reading; Professor Neumann, Drs Cossey, Kovacs, MeDougall, Praeger, Pride, Rangaswamy and Stewart. I here reeord my thanks to all these people for their lightening of the editorial burden. M.F. Newrnan CONTENTS 1 Introduction . . 8 yan, Periodic groups of odd exponent Reinhold Baer, Einbettungseigenschaften von Normalteilern: der Schluss vom 13 Endlichen aufs Unendliche D.W. Barnes, Characterisation of the groups with the Gaschutz cohomology property 63 Gi Ibert Baumslag, Finitely presented metabe1ian groups 65 Gi Ibert Baumslag, Some problems on one-relator groups 75 A.J. Ba, J. Kautsky and J.W. Wamsley, Computation in nilpotent groups (application) 82 Wi I I iam W. Boone, Between logic and group theory 90 Richard Brauer, On the structure of blocks of characters of finite groups 103 A.M. Brunner, Transitivity-systems of certain one-relator groups 131 Egg8r M. Bryant, Characteristic subgroups of free groups 141 y, Metabe1ian varieties of groups 150 R.A. Bryce and John Cossey, Subdirect product c10sed Fitting c1asses 158 R.G." This volume consists of papers presented to the Second International Conference on the Theory of Groups held in Canberra in August 1973 together with areport by the chairman of the Organizing Committee and a collection of problems. The manuscripts were typed by Mrs Geary, the bulk of the bibliographie work was done by Mrs Pinkerton, and a number of colleagues helped with proof-reading; Professor Neumann, Drs Cossey, Kovacs, MeDougall, Praeger, Pride, Rangaswamy and Stewart. I here reeord my thanks to all these people for their lightening of the editorial burden. M.F. Newrnan CONTENTS 1 Introduction . . 8 ~yan, Periodic groups of odd exponent Reinhold Baer, Einbettungseigenschaften von Normalteilern: der Schluss vom 13 Endlichen aufs Unendliche D.W. Barnes, Characterisation of the groups with the Gaschütz cohomology property 63 Gi Ibert Baumslag, Finitely presented metabe1ian groups 65 Gi Ibert Baumslag, Some problems on one-relator groups 75 A.J. Ba~, J. Kautsky and J.W. Wamsley, Computation in nilpotent groups (application) 82 Wi I I iam W. Boone, Between logic and group theory 90 Richard Brauer, On the structure of blocks of characters of finite groups 103 A.M. Brunner, Transitivity-systems of certain one-relator groups 131 Egg8r M. Bryant, Characteristic subgroups of free groups 141 ~y~, Metabe1ian varieties of groups 150 R.A. Bryce and John Cossey, Subdirect product c10sed Fitting c1asses 158 R.G