This is the first book to contain a rigorous construction and uniqueness proof for the largest and most famous sporadic simple group, the Monster. The author provides a systematic exposition of the theory of the Monster group, which remains largely unpublished despite great interest from both mathematicians and physicists due to its intrinsic connection with various areas in mathematics, including reflection groups, modular forms and conformal field theory. Through construction via the Monster amalgam – one of the most promising in the modern theory of finite groups – the author observes some important properties of the action of the Monster on its minimal module, which are axiomatized under the name of Majorana involutions. Development of the theory of the groups generated by Majorana involutions leads the author to the conjecture that Monster is the largest group generated by the Majorana involutions.
This is the second volume in a two-volume set, which provides a complete self-contained proof of the classification of geometries associated with sporadic simple groups: Petersen and tilde geometries. The second volume contains a study of the representations of the geometries under consideration in GF(2)-vector spaces as well as in some non-abelian groups. The central part is the classification of the amalgam of maximal parabolics, associated with a flag transitive action on a Petersen or tilde geometry. The classification is based on the method of group amalgam, the most promising tool in modern finite group theory. Via their systematic treatment of group amalgams, the authors establish a deep and important mathematical result. This book will be of great interest to researchers in finite group theory, finite geometries and algebraic combinatorics.
This book is the first volume in a two-volume set, which will provide the complete proof of classification of two important classes of geometries, closely related to each other: Petersen and tilde geometries. There is an infinite family of tilde geometries associated with non-split extensions of symplectic groups over a field of two elements. Besides that there are twelve exceptional Petersen and tilde geometries. These exceptional geometries are related to sporadic simple groups, including the famous Monster group and this volume gives a construction for each of the Petersen and tilde geometries which provides an independent existence proof for the corresponding automorphism group. Important applications of Petersen and Tilde geometries are considered, including the so-called Y-presentations for the Monster and related groups, and a complete indentification of Y-groups is given. This is an essential purchase for researchers into finite group theory, finite geometries and algebraic com
Transforming NATO: New Allies, Missions and Capabilities, by Ivan Dinev Ivanov, reveals that in order to understand the complexity of NATO's transformation, one must explore the management of allied r
American short-story writer Andre Dubus (1936–1999) was a “writer’s writer.” His acclaimed collections of short stories and essays involve one or all of three thematic discourses—that of the Catholic
Transforming NATO: New Allies, Missions and Capabilities, by Ivan Dinev Ivanov, reveals that in order to understand the complexity of NATO's transformation, one must explore the management of allied r
This book is the first volume in a two-volume set, which will provide the complete proof of classification of two important classes of geometries, closely related to each other: Petersen and tilde geometries. There is an infinite family of tilde geometries associated with non-split extensions of symplectic groups over a field of two elements. Besides that there are twelve exceptional Petersen and tilde geometries. These exceptional geometries are related to sporadic simple groups, including the famous Monster group and this volume gives a construction for each of the Petersen and tilde geometries which provides an independent existence proof for the corresponding automorphism group. Important applications of Petersen and Tilde geometries are considered, including the so-called Y-presentations for the Monster and related groups, and a complete indentification of Y-groups is given. This is an essential purchase for researchers into finite group theory, finite geometries and algebraic com
Join the world's greatest detective, Nate the Great, as he solves the mystery of the missing tomatoes in this long-running chapter book series that's makes problem-solving fun!HOW DOES YOUR GARDEN GROW?A friendly competition to grow the best organic garden is underway. The prize is tempting . . . a ribbon, a photo and article in the newspaper, AND some all-you-can eat favorites from Ned’s Diner!Esmeralda, Annie, Oliver, and Rosamond are among the competitors. Just a few days before contest judging, some of Rosamond’s tomatoes go missing and Nate and Sludge are called to investigate.Who is eager for tomatoes, and why? Nate and Sludge are on the case and what they find surprises all but makes perfect sense!
