{"product_id":"finite-groups-iii-grundlehren-der-mathematischen-wissenschaften","title":"Finite Groups III (Grundlehren der mathematischen Wissenschaften)","description":"\u003cp\u003eOur review of Finite Groups III finds it to be an advanced and historically important volume for researchers and graduate students focused on the structural theory of finite groups. This final volume in the series addresses developments from the 1960s, including local methods that grew out of the proof of Burnside's odd order theorem and the role of the generalized Fitting subgroup, making it valuable as a reference and as a bridge between classical transfer theory and midcentury innovations in group classification.\u003c\/p\u003e\u003ch2\u003eKey Features\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eHistorical scope:\u003c\/strong\u003e The book surveys important developments of the 1960s that shaped modern finite group theory, helping readers place later results in context.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eLocal theory coverage:\u003c\/strong\u003e Chapters discuss local methods that emerged from the early stages of the odd order theorem, providing insight into techniques used in classification work.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eContinuation of transfer theory:\u003c\/strong\u003e Builds on earlier chapters on the transfer, making the text useful for readers following the series' internal development of ideas.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eIntroduction of generalized Fitting subgroup:\u003c\/strong\u003e Presents the generalized Fitting subgroup and its role in character theory and structure, clarifying a concept central to later research.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eScholarly authorship:\u003c\/strong\u003e Written by B. Huppert and N. Blackburn, the text reflects expertise and is aimed at an audience comfortable with rigorous algebraic exposition.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch2\u003eWho It's For\u003c\/h2\u003e\u003cp\u003eFinite Groups III is best for graduate students, researchers, and advanced readers in algebra who want a deeper understanding of mid-20th-century advances in finite group theory and the technical apparatus that preceded the classification of finite simple groups. It is particularly useful for readers tracing the development of local methods and the generalized Fitting subgroup.\u003c\/p\u003e\u003cp\u003eThose seeking an introductory or problem-driven textbook should look elsewhere: the exposition assumes prior familiarity with group theory and earlier volumes or comparable literature, and it is not a beginner-level treatment.\u003c\/p\u003e\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eAuthoritative historical perspective that connects classical transfer theory to later structural advances.\u003c\/li\u003e\n\u003cli\u003eClear presentation of local theory ideas that arose during the proof efforts for Burnside's conjecture.\u003c\/li\u003e\n\u003cli\u003eValuable discussion of the generalized Fitting subgroup for researchers studying character and structure theory.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eNot suitable as an introductory text; the material assumes substantial prior knowledge.\u003c\/li\u003e\n\u003cli\u003eSome proofs and topics are outlined rather than presented in full detail, reflecting the book's survey and continuity purpose.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch2\u003eSpecifications\u003c\/h2\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eFinite Groups III (Grundlehren der mathematischen Wissenschaften)\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthors\u003c\/td\u003e\n\u003ctd\u003eB. Huppert, N. Blackburn\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSubject\u003c\/td\u003e\n\u003ctd\u003eFinite group theory; local methods and structure\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFocus areas\u003c\/td\u003e\n\u003ctd\u003eTransfer theory continuation; generalized Fitting subgroup; 1960s developments\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIntended audience\u003c\/td\u003e\n\u003ctd\u003eGraduate students and researchers in algebra\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eGrundlehren der mathematischen Wissenschaften\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\u003ch2\u003eOur Verdict\u003c\/h2\u003e\u003cp\u003eFinite Groups III is a worthwhile purchase for anyone researching the evolution of finite group theory or needing a concise presentation of the local methods that emerged in the 1960s. It offers important context and technical discussion valuable to specialists, though readers seeking elementary exposition should consult more introductory texts first.\u003c\/p\u003e\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003eIs this book suitable for beginners?\u003c\/strong\u003e\u003cbr\u003eThe book assumes prior graduate-level familiarity with group theory and earlier foundational material, so it is not recommended for beginners.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eDoes it contain full proofs of the Burnside odd order theorem?\u003c\/strong\u003e\u003cbr\u003eNo, the volume discusses ideas from early stages of that proof and related local theory but does not present the full long proof.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWho authored this work?\u003c\/strong\u003e\u003cbr\u003eThe book is authored by B. Huppert and N. Blackburn and appears in the Grundlehren der mathematischen Wissenschaften series.\u003c\/p\u003e","brand":"B. Huppert, N. Blackburn","offers":[{"title":"Default Title","offer_id":48240135143643,"sku":"3642679994","price":128.97,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/51A0XRbEQTL._SL1259.jpg?v=1770991927","url":"https:\/\/gearmusthave.com\/products\/finite-groups-iii-grundlehren-der-mathematischen-wissenschaften","provider":"GearMustHave","version":"1.0","type":"link"}