Infinite Permutation Groups

This is a transcript of a lecture course on Infinite Permutation Groups given by Peter M. Neumann (1940-2020) in Oxford during the academic year 1988-1989. The field of Infinite Permutation Groups only emerged as an independent field of study in the 1980's. Most of the results described in these notes were at the time of the lectures brand new and had either just recently appeared in print or had not appeared formally. A large part of the results described is either due to Peter himself or heavily influenced by him. These notes offer Peter's personal take on a field that he was instrumental in creating and in many cases ideas and questions that can not be found in the published literature.Comment: The text of [v1] and [v2] is identical. [v1] is formatted so that each new lecture starts at a right hand page (127+v pages) and [v2] is formatted without all the extra page breaks (93+v pages). Edited by David A. Craven (Birmingham), Dugald Macpherson (Leeds) and R\"ognvaldur G. M\"oller (Reykjav\'ik). Comments and corrections can be sent to R\"oggi M\"oller ([email protected]

Canada\u27s New Gun Control Legislation: Stiffer Penalties and Controlled Access

On December 6, 1989, fourteen women were murdered at the École Polytechnique in Montreal by a gunman equipped with a legally acquired semi-automatic paramilitary rifle and a large capacity clip magazine. Although the weapon was advertised by its manufacturers, Sturm, Ruger and Co. of Connecticut, as ideal for law enforcement , it was popular with hunters and was readily available at stores. The gunman\u27s rampage provoked an unprecedented outcry for stricter gun control laws in Canada. While revisions to the firearms provisions of the Criminal Code were already being considered, the tragedy reopened gun control debate and committed federal legislators to a firm timetable for enacting new legislation. On the eve of the second anniversary of the women\u27s deaths Bill C-17, which contained a substantial number of amendments to the firearms section of the Criminal Code, was given royal assent. In this paper I will attempt to analyse the Bill C-17 amendments from two perspectives: accessibility to, and availability of, firearms. Controlling accessibility entails tightening the screening processes for gun procurement whereas circulation and regulating availability involves reducing the number of weapons in possession and circulation. These two approaches also represent divided perspectives in the community. Generally, gun owners and their supporters favour access controls, which leave legitimate purchasers free to buy and own as many weapons as they wish, while people wishing to move towards a gun free society support access controls coupled with a reduction in the numbers of available weapons. With Bill C-17 Parliament has attempted to increase controls on access to firearms and stiffen penalties for weapons related offences. Provisions directly affecting the availability of firearms – which depend mostly on the classification of weapons, as either prohibited or restricted – remain by and large unchanged. Thus, although large capacity clip magazines, like those used by the gunman in Montreal, are now prohibited, semi-automatic rifles remain classified as non-restricted firearms. Together with any number of smaller capacity magazines, they can still be purchased in unlimited quantities

Primitive permutation groups of degree 3p

This paper presents an analysis of primitive permutation groups of degree $3p$, where $p$ is a prime number, analogous to H. Wielandt's treatment of groups of degree $2p$. It is also intended as an example of the systematic use of combinatorial methods as surveyed in \S6 for distilling information about a permutation group from knowledge of the decomposition of its character. The work is organised into three parts. Part I contains the lesser half of the calculation, the determination of the decomposition of the permutation character. Part II contains a survey of the combinatorial methods and, based on these methods, the major part of the calculation. Part III ties up loose ends left earlier in the paper and gives a tabulation of detailed numerical results.Comment: Unpublished paper from 1969. Afterword by Peter J. Cameron explains the contex

Peace Bonds: Preventive Justice? Or Preventing Justice?

In this comment I wish to examine some of the legal and practical problems with peace bond proceedings under s. 810 of the Criminal Code for women who seek to protect themselves from their abusive partners. Recent research confirms that women are most likely to suffer violence at the hands of men they have known intimately and that they are especially vulnerable at the time of separation. A 1991 study funded by the Ontario Women\u27s Directorate and the Ontario Ministry of Community and Social Services, for example, found that intimate femicides – or the killing of women by their intimate partners – accounted for some 61 percent of all homicides of women where an offender was identified. In sharp contrast, only eight percent of all male victims were killed by their spouses. Women separating or recently estranged from their partners were at the greatest risk, homicide being significantly more likely to occur at this time than at other times during the relationship

Impact of Electric Fields on Highly Excited Rovibrational States of Polar Dimers

We study the effect of a strong static homogeneous electric field on the highly excited rovibrational levels of the LiCs dimer in its electronic ground state. Our full rovibrational investigation of the system includes the interaction with the field due to the permanent electric dipole moment and the polarizability of the molecule. We explore the evolution of the states next to the dissociation threshold as the field strength is increased. The rotational and vibrational dynamics are influenced by the field; effects such as orientation, angular motion hybridization and squeezing of the vibrational motion are demonstrated and analyzed. The field also induces avoided crossings causing a strong mixing of the electrically dressed rovibrational states. Importantly, we show how some of these highly excited levels can be shifted to the continuum as the field strength is increased, and reversely how two atoms in the continuum can be brought into a bound state by lowering the electric field strength.Comment: 10 pages, 4 figure

Embedding in a Finite 2-Generator Semigroup

We augment the body of existing results on embedding finite semigroups of a certain type into 2-generator finite semigroups of the same type. The approach adopted applies to finite semigroups the idempotents of which form a band and also to finite orthodox semigroups

Some infinite permutation groups and related finite linear groups

This article began as a study of the structure of infinite permutation groups G in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point stabilisers are merely assumed to satisfy min-n, the minimal condition on normal subgroups. The groups G are then of two kinds. Either they have a maximal finite normal subgroup, modulo which they have either one or two minimal non-trivial normal subgroups, or they have a regular normal subgroup M which is a divisible abelian p-group of finite rank. In the latter case the point stabilisers are finite and act irreducibly on a p-adic vector space associated with M. This leads to our second variation, which is a study of the finite linear groups that can arise