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020 _a9783031544613
_9978-3-031-54461-3
024 7 _a10.1007/978-3-031-54461-3
_2doi
050 4 _aQA174-183
072 7 _aPBG
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBG
_2thema
100 1 _avan Beek, Martin.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_975433
245 1 0 _aRank 2 Amalgams and Fusion Systems
_h[electronic resource] /
_cby Martin van Beek.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aVII, 206 p. 2 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2343
505 0 _aIntroduction -- Preliminaries -- Fusion Systems -- Amalgams in Fusion Systems -- The Amalgam Method -- Zα′ ̸≤ Qα -- Zα′ ≤ Qα.
520 _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.
650 0 _aGroup theory.
_970149
650 0 _aAlgebraic topology.
650 0 _aGraph theory.
650 1 4 _aGroup Theory and Generalizations.
_970154
650 2 4 _aAlgebraic Topology.
650 2 4 _aGraph Theory.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031544606
776 0 8 _iPrinted edition:
_z9783031544620
830 0 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2343
_975434
856 4 0 _uhttps://doi.org/10.1007/978-3-031-54461-3
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-LNM
999 _c59236
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