Homological finiteness properties of monoids, their ideals and maximal subgroups

We consider the general question of how the homological finiteness property left-FPn holding in a monoid influences, and conversely depends on, the property holding in the substructures of that monoid. In particular we show that left-FPn is inherited by the maximal subgroups in a completely simple minimal ideal, in the case that the minimal ideal has finitely many left ideals. For completely simple semigroups we prove the converse, and as a corollary show that a completely simple semigroup is of type left- and right-FPn if and only if it has finitely many left and right ideals and all of its maximal subgroups are of type FPn. Also, given an ideal of a monoid, we show that if the ideal has a two-sided identity element then the containing monoid is of type left-FPn if and only if the ideal is of type left-FPn.Comment: 25 page

Automorphisms of real Lie algebras of dimension five or less

The Lie algebra version of the Krull-Schmidt Theorem is formulated and proved. This leads to a method for constructing the automorphisms of a direct sum of Lie algebras from the automorphisms of its indecomposable components. For finite-dimensional Lie algebras, there is a well-known algorithm for finding such components, so the theorem considerably simplifies the problem of classifying the automorphism groups. We illustrate this by classifying the automorphisms of all indecomposable real Lie algebras of dimension five or less. Our results are presented very concisely, in tabular form

Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids

This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoids, hypoplactic monoids, and sylvester monoids. For Chinese monoids, we first give new presentations via finite complete rewriting systems, using more lucid constructions and proofs than those given independently by Chen & Qui and Güzel Karpuz; we then construct biautomatic structures. For hypoplactic monoids, we construct finite complete rewriting systems and biautomatic structures. For sylvester monoids, which are not finitely presented, we prove that the standard presentation is an infinite complete rewriting system, and construct biautomatic structures. Consequently, the monoid algebras corresponding to monoids of these classes are automaton algebras in the sense of Ufnarovskij

A Svarc-Milnor lemma for monoids acting by isometric embeddings

We continue our programme of extending key techniques from geometric group theory to semigroup theory, by studying monoids acting by isometric embeddings on spaces equipped with asymmetric, partially-defined distance functions. The canonical example of such an action is a cancellative monoid acting by translation on its Cayley graph. Our main result is an extension of the Svarc-Milnor Lemma to this setting.Comment: 11 page

KSC Facilities Status and Planned Management Operations

This is a status report on the facilities and planned operations at the Kennedy Space Center that will support Space Shuttle launches, the first of which is now scheduled for late 1979. The facilities are essentially complete, with all new construction and modifications to existing buildings almost finished. Some activity is still in progress at Pad A and on the Mobile Launcher, due to changes in requirements, but is not expected to impact the launch schedule. The installation and testing of the ground checkout equipment that will be used to test the fIight hardware is now in work. The Launch Processing System is currently supporting the development of the applications software that will perform the testing of this fIight hardware. The Shuttle Program is unique to past manned space programs in that very tight budgetary constraints have been imposed in an effort to keep the costs low. For KSC, this means adopting a philosophy of launch-to-cost. In an era of routine space flight, this presents a very real challenge to management; the necessity of controlling costs while maintaining tight schedules. An overview of how this management challenge is to be met will be presented

Psychopathy and impulsivity: The relationship of psychopathy to different aspects of UPPS-P impulsivity

Impulsivity is thought to be a major component of psychopathy. However, impulsivity is a multi-faceted concept, and different facets may have differential relationships to psychopathy. We measured impulsivity via the UPPS-P in a sample of prisoners and in patients in a personality disorder service resident in secure psychiatric care. Psychopathy in the prison sample was measured via the clinician-rated Psychopathy Checklist: Screening Version and in the patients via the Psychopathy Checklist-Revised. We found that the Lifestyle/Antisocial factor (Factor 2) was associated with acting rashly when emotional (Negative Urgency and Positive Urgency). However, the Interpersonal/Affective factor (Factor 1) was associated with reduced impulsivity in the domains of premeditation and perseverance, and its unique variance was also associated with less rash behaviour. The Interpersonal facet (Facet 1) was particularly associated with reduced impulsivity. The results show that individuals with high Interpersonal traits of psychopathy can plan carefully and are persistent in their goals. This may underpin instrumental violence and criminal behaviour. Thus, a simple unitary understanding of the relationship between psychopathy and impulsivity may not be valid and may distort the multifaceted relationship between the two concepts that could assist in the assessment and management of psychopathic offenders