Proceedings of the Second International Conference on the Theory of Groups

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.

Periodic groups of odd exponent.- Einbettungseigenschaften von Normalteilern: Der Schluss vom Endlichen aufs Unendliche.- Characterisation of the groups with the Gaschütz cohomology property.- Finitely presented metabelian groups.- Some problems on one-relator groups.- Computation in nilpotent groups (application).- Between logic and group theory.- On the structure of blocks of characters of finite groups.- Transitivity-systems of certain one-relator groups.- Characteristic subgroups of free groups.- Metabelian varieties of groups.- Subdirect product closed fitting classes.- On the rank of the intersection of subgroups of a fuchsian group.- Subgroups of binary relations.- The 2-adic representations of Klein's four group.- A general purpose group theory program.- On the modular representations of the general linear and symmetric groups.- Words which give rise to another group operation for a given group.- Classes of finite soluble groups.- A note on blocks.- The subgroup theorem for amalgamated free products, HNN-constructions and colimits.- Linear representations over principal ideal domains.- A property common to the Weyl and orthogonal groups.- Primitive extensions of maximal diameter of multiply transitive permutation groups.- Some characters of orthogonal groups over the field of two elements.- Type sets and admissible multiplications.- Power series and matrix representations of certain relatively free groups.- The nilpotency class of finitely generated groups of exponent four.- Hypocritical and sincere groups.- Sylow subgroups of locally finite groups.- A reidemeister-schreier program.- Non-nilpotent groups with normalizer condition.- The influence of 2-sylow intersections on the structure of finite simple groups.- Rank four configurations.- Some nonsimplicity criteria for finite groups.- Free subgroups of free topological groups.- Some questions in the theory of soluble groups.- Locally finite simple groups.- Normal subgroups of groups of prime-power order.- Some related questions in the theory of groups and lie algebras.- Hanna Neumann's problems on varieties of groups.- Finite projective planes and sharply 2-transitive subsets of finite groups.- Non Euclidean crystallographic groups.- On subnormality in soluble minimax groups.- Varieties generated by finite algebras.- Computing with finite simple groups.- Compact torsion groups.- Braid groups: A survey.- Two-bridge knots have residually finite groups.- Periodic automorphisms of the two-generator free group.- On groups of exponent four: A criterion for nonsolvability.- The topology of free products of topological groups.- Some groups I have known.- Transitive permutation groups of prime degree.- Ideals in the centre of a group ring.- A non-distributive metabelian variety lattice.- Polynomial maps.- Über Erzeugende Ebener Diskontinuierlicher Gruppen.- Contribution to the theory of abstract groups.- Sylow subgroups of finite permutation groups.- On the Nielsen equivalence of pairs of generators in certain HNN groups.- The collineation groups of finite generalized hall planes.- Abelian groups with self-injective endomorphism rings.- Lattice isomorphisms and saturated formations of finite soluble groups.- Some reflections on HNN extensions.- Amalgames et points fixes.- Geometric characterizations in finite group theory.- Torsion-free metabelian groups with infinite cyclic quotient groups.- On the lie ring of a group of prime exponent.- Computation in nilpotent groups (theory).- On groups admitting an elementary Abelian automorphism group.- Varieties described by verbal subgroups.- A relation in free products.- A note on subsoluble groups.- On generalized soluble groups.- Finite groups with sylow 2-subgroups of type the alternating group of degree sixteen.- Problem section.