The author classifies all reduced, indecomposable fusion systems over finite -groups of sectional rank at most . The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional -rank at most . But this method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.

For a finite group G of Lie type and a prime p, the authors compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic, with a very short list of exceptions. When p is different from the defining characteristic, the situation is much more complex but can always be reduced to a case where the natural map from Out(G) to outer automorphisms of the fusion or linking system is split surjective. This work is motivated in part by questions involving extending the local structure of a group by a group of automorphisms, and in part by wanting to describe self homotopy equivalences of BG∧p in terms of Out(G).

In around 1980, G. Mason announced the classification of a subclass of an important class of finite simple groups known as 'quasithin groups'. In the main theorem of this two-part work the authors provide a proof of a stronger theorem classifying a larger class of groups independently of Mason's research.

This book is intended to help explore the field of smart sustainable cities in its complexity, heterogeneity, and breadth, the many faces of a topical subject of major importance for the future that encompasses so much of modern urban life in an increasingly computerized and urbanized world. Indeed, sustainable urban development is currently at the center of debate in light of several ICT visions becoming achievable and deployable computing paradigms, and shaping the way cities will evolve in the future and thus tackle complex challenges. This book integrates computer science, data science, complexity science, sustainability science, system thinking, and urban planning and design. As such, it contains innovative computer–based and data–analytic research on smart sustainable cities as complex and dynamic systems. It provides applied theoretical contributions fostering a better understanding of such systems and the synergistic relationships between the underlying physical and informational landscapes. It offers contributions pertaining to the ongoing development of computer–based and data science technologies for the processing, analysis, management, modeling, and simulation of big and context data and the associated applicability to urban systems that will advance different aspects of sustainability. This book seeks to explicitly bring together the smart city and sustainable city endeavors, and to focus on big data analytics and context-aware computing specifically. In doing so, it amalgamates the design concepts and planning principles of sustainable urban forms with the novel applications of ICT of ubiquitous computing to primarily advance sustainability. Its strength lies in combining big data and context–aware technologies and their novel applications for the sheer purpose of harnessing and leveraging the disruptive and synergetic effects of ICT on forms of city planning that are required for future forms of sustainable development. This is because the effects of such technologies reinforce one another as to their efforts for transforming urban life in a sustainable way by integrating data–centric and context–aware solutions for enhancing urban systems and facilitating coordination among urban domains. This timely and comprehensive book is aimed at a wide audience across science, academia industry, and policymaking. It provides the necessary material to inform relevant research communities of the state–of–the–art research and the latest development in the area of smart sustainable urban development, as well as a valuable reference for planners, designers, strategists, and ICT experts who are working towards the development and implementation of smart sustainable cities based on big data analytics and context–aware computing.

The emerging technology of multisensor data fusion has a wide range of applications, both in Department of Defense (DoD) areas and in the civilian arena. The techniques of multisensor data fusion draw from an equally broad range of disciplines, including artificial intelligence, pattern recognition, and statistical estimation. With the rapid evolut

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A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.