01749cam a22002414a 4500008004100000020001800041020001500059040000800074050002500082100002500107245009200132260006400224300001900288490005900307500002000366505001700386520097800403650003201381650002401413650002401437700001901461700002701480110504s2011    enka          001 0 eng    a9781107601000  a1107601002  aSDU00aQA182.5bA812 F 20111 aAschbacher, Michael.10aFusion systems in algebra and topology /cMichael Aschbacher, Radha Kessar, Bob Oliver.  aCambridge ;aNew York :bCambridge University Press,c2011.  a320 p. :bill.1 aLondon mathematical society lecture note series ;v391  aIncludes index.  aHKBU Library  a"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. The book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians"-- 0aCombinatorial group theory. 0aTopological groups. 0aAlgebraic topology.1 aKessar, Radha.1 aOliver, Robert,d1949-