Enumeration of finite groups / / Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman [[electronic resource]]

• Record Nr.: UNINA9910452090003321
• Autore: Blackburn Simon R.
• Pubbl/distr/stampa: Cambridge : , : Cambridge University Press, , 2007
• ISBN: 1-107-18521-1; 1-281-15366-4; 9786611153663; 1-139-13345-4; 0-511-35537-8; 0-511-35487-8; 0-511-35429-0; 0-511-54275-5; 0-511-35589-0
• Descrizione fisica: 1 online resource (xii, 281 pages) : digital, PDF file(s)
• Collana: Cambridge tracts in mathematics ; ; 173
• Disciplina: 512.23
• Soggetti: Finite groups
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Some basic observations -- Preliminaries -- Enumerating p-groups: a lower bound -- Enumerating p-groups: upper bounds -- Some more preliminaries -- Group extensions and cohomology -- Some representation theory -- Primitive soluble linear groups -- The orders of groups -- Conjugacy classes of maximal soluble subgroups of symmetric groups -- Enumeration of finite groups with abelian Sylow subgroups -- Maximal soluble linear groups -- Conjugacy classes of maximal soluble subgroups of the general linear groups -- Pyber's theorem: the soluble case -- Pyber's theorem: the general case -- Enumeration within varieties of abelian groups -- Enumeration within small varieties of A-groups -- Enumeration within small varieties of p-groups.
• Sommario/riassunto: How many groups of order n are there? This is a natural question for anyone studying group theory, and this Tract provides an exhaustive ; and up-to-date account of research into this question spanning almost fifty years. The authors presuppose an undergraduate knowledge of group theory, up to and including Sylow's Theorems, a little knowledge of how a group may be presented by generators and relations, a very little representation theory from the perspective of module theory, and a very little cohomology theory - but most of the basics are expounded here and the book is more or less self-contained. Although it is principally devoted to a connected exposition of an agreeable theory, the book does also contain some material that has not hitherto been published. It is designed to be used as a graduate text but also as a handbook for established research workers in group theory.