{"product_id":"subgroup-growth-progress-in-mathematics-comprehensive-group-theory","title":"Subgroup Growth (Progress in Mathematics) - Comprehensive Group Theory","description":"\u003cp\u003eIn this review of Subgroup Growth (Progress in Mathematics), the reviewer finds a deep, scholarly treatment of how subgroups of finite index distribute in groups and why that distribution matters. Geared toward researchers and advanced graduate students, the book's single biggest reason to buy is its systematic synthesis of recent developments linking subgroup growth to algebraic structure across multiple areas of mathematics. This review explains who will benefit from the book, what its strengths are, and what limitations a general reader should expect when approaching this specialized text.\u003c\/p\u003e\u003ch2\u003eKey Features\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eComprehensive scope:\u003c\/strong\u003e The book gathers two decades of research into a coherent narrative so readers can follow the development of subgroup growth as a field.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eConnections across disciplines:\u003c\/strong\u003e It highlights links between subgroup growth and topics such as finite simple groups, permutation groups and p-adic methods to give readers broader context for results.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFocus on growth types:\u003c\/strong\u003e The text explains how possible growth rates for finitely generated groups are determined, helping specialists classify group behavior.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eStructure versus growth:\u003c\/strong\u003e Emphasis on tight connections between algebraic structure and subgroup growth equips researchers to infer structural properties from counting data.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eSystematic exposition:\u003c\/strong\u003e The authors present proofs and arguments in a way that helps experienced readers trace the logical development of the subject rather than relying on scattered papers.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch2\u003eWho It's For\u003c\/h2\u003e\u003cp\u003eSubgroup Growth is best suited to mathematicians working in infinite group theory, graduate students specializing in algebra, and researchers who require a consolidated account of subgroup growth results. The book serves as a reference for those investigating how subgroup counts reflect structural features and for readers needing pointers to the literature across related areas.\u003c\/p\u003e\u003cp\u003eThose seeking an introductory textbook or casual reading on group theory should look elsewhere, since the material presumes familiarity with advanced algebra, finite simple groups and related tools. It is not tailored to beginners or to applications-focused audiences without a strong theoretical background.\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 synthesis of a rapidly developing area that saves readers from tracking numerous separate papers.\u003c\/li\u003e\n\u003cli\u003eClear emphasis on the relationship between subgroup growth and algebraic structure, useful for theoretical insight.\u003c\/li\u003e\n\u003cli\u003eInterdisciplinary references that place subgroup growth within the broader landscape of finite simple groups and permutation group theory.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\u003cli\u003eHighly specialized and assumes advanced background, making it unsuitable for non-experts or beginners.\u003c\/li\u003e\u003c\/ul\u003e\u003ch2\u003eSpecifications\u003c\/h2\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eSubgroup Growth (Progress in Mathematics)\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthors\u003c\/td\u003e\n\u003ctd\u003eAlexander Lubotzky, Dan Segal\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSubject\u003c\/td\u003e\n\u003ctd\u003eSubgroup growth and infinite group theory\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eScope\u003c\/td\u003e\n\u003ctd\u003eDistribution of subgroups of finite index and growth types\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eInterdisciplinary links\u003c\/td\u003e\n\u003ctd\u003eFinite simple groups, permutation groups, p-adic and algebraic methods\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAudience\u003c\/td\u003e\n\u003ctd\u003eResearchers and advanced graduate students in algebra\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\u003ch2\u003eOur Verdict\u003c\/h2\u003e\u003cp\u003eSubgroup Growth is a valuable, well-organized reference for specialists who need a thorough account of subgroup distribution and its algebraic implications. While not accessible to beginners, its synthesis of results and cross-disciplinary perspective make it good value for researchers and advanced students seeking a single, reliable source on this active area of group theory.\u003c\/p\u003e\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003eDoes this book require prior graduate-level algebra?\u003c\/strong\u003e\u003cbr\u003eYes. The text assumes familiarity with infinite group theory, finite simple groups and advanced algebraic concepts.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eIs the book mainly theoretical or application oriented?\u003c\/strong\u003e\u003cbr\u003eThe focus is theoretical: it develops the mathematical theory of subgroup growth and connections to algebraic structure rather than practical applications.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWho are the authors and why does that matter?\u003c\/strong\u003e\u003cbr\u003eAlexander Lubotzky and Dan Segal are established researchers in group theory, and their expertise ensures a rigorous, well-informed synthesis of the field.\u003c\/p\u003e","brand":"Alexander Lubotzky, Dan Segal","offers":[{"title":"Default Title","offer_id":48246745170139,"sku":"3034898460","price":59.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/716agYj8vvL._SL1323.jpg?v=1776266975","url":"https:\/\/gearmusthave.com\/products\/subgroup-growth-progress-in-mathematics-comprehensive-group-theory","provider":"GearMustHave","version":"1.0","type":"link"}