03373nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202072001500225100008600240245008500326250001800411264006900429300004300498336002600541337002600567338003600593347002400629490005300653505014300706520157800849650002502427650002402452650001802476650004502494650002402539650001802563710003402581773002602615776003602641776003602677830006002713856004602773912001402819912001502833912001402848999001702862978-3-031-54461-3DE-He21320251030112001.0cr nn 008mamaa240419s2024    sz |    s    |||| 0|eng d  a97830315446139978-3-031-54461-37 a10.1007/978-3-031-54461-32doi 4aQA174-183 7aPBG2bicssc 7aMAT0020102bisacsh 7aPBG2thema1 avan Beek, Martin.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97543310aRank 2 Amalgams and Fusion Systemsh[electronic resource] /cby Martin van Beek.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aVII, 206 p. 2 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLecture Notes in Mathematics,x1617-9692 ;v23430 aIntroduction -- Preliminaries -- Fusion Systems -- Amalgams in Fusion Systems -- The Amalgam Method -- Zα′ ̸≤ Qα -- Zα′ ≤ Qα.  aThis monograph provides a comprehensive treatment of the classification of small fusion systems, that is, fusion systems with few essential subgroups. It demonstrates a broad range of techniques from local group theory and fusion systems, several of which can be applied in more general settings. Addressing research problems that have not been treated in the past, it is the first text to explicitly use the amalgam method in this context. Fusion systems offer an enticing way to unify various p-local methods employed in group theory, representation theory and homotopy theory; but as abstract constructions they are still somewhat mysterious. This book paves the way to a broad and systematic study of these categories by applying the amalgam method, thus modernizing a methodology widely used to understand the local structure of finite groups. With this comes an introduction to several vital techniques in local group theory, a generous survey of the structure and modular representation theory of some important families of finite groups, and a demonstration of the value of combinatorial methods in finite group theory and fusion systems. Primarily aimed at researchers active in fusion systems and group amalgams, the book will also be of interest to anyone working with finite groups and their modular representations, group actions on trees, or classifying spaces. The inclusion of preliminary chapters outlining the theoretical prerequisites make it ideal for a short lecture course or as a reading group text for early career researchers and graduate students. 0aGroup theory.970149 0aAlgebraic topology. 0aGraph theory.14aGroup Theory and Generalizations.97015424aAlgebraic Topology.24aGraph Theory.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303154460608iPrinted edition:z9783031544620 0aLecture Notes in Mathematics,x1617-9692 ;v234397543440uhttps://doi.org/10.1007/978-3-031-54461-3  aZDB-2-SMA  aZDB-2-SXMS  aZDB-2-LNM  c59236d59236