{"product_id":"profinite-groups-authoritative-introduction-and-reference","title":"Profinite Groups - Authoritative Introduction and Reference","description":"\u003cp\u003eIn this review of Profinite Groups the book is recommended for graduate students and researchers who need a clear, self-contained introduction to profinite groups and a durable reference. The single biggest reason to buy is its balance of accessible exposition and depth: it covers foundational material while emphasizing free constructions, and the second edition adds new appendices that update the theory of free profinite groups. Readers will find both basic facts and specialist tools in one volume, making it practical for learning and for consultation during research.\u003c\/p\u003e\u003ch2\u003eKey Features\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eSelf-contained exposition:\u003c\/strong\u003e The text develops profinite groups from basic facts to advanced topics so a reader can follow without extensive external prerequisites.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFree constructions emphasis:\u003c\/strong\u003e Detailed treatment of free profinite groups and the structure of their subgroups gives concrete tools for constructing and analysing examples.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eConnections to Galois theory:\u003c\/strong\u003e The book shows why \u003cstrong\u003eprofinite groups are Galois groups\u003c\/strong\u003e, which is valuable for algebraic number theory contexts.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eHomology and cohomology coverage:\u003c\/strong\u003e Homological methods are described with a minimum of prerequisites, making these techniques accessible to more readers.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eUpdated second edition:\u003c\/strong\u003e Three new appendices include a new characterization of free profinite groups, strengthening the volume as a modern reference.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch2\u003eWho It's For\u003c\/h2\u003e\u003cp\u003eThis book is best for advanced undergraduates, graduate students, and professional mathematicians working in algebraic number theory, group theory, or related areas who need a rigorous introduction and a reference that treats both foundations and specialized constructions. Its self-contained nature makes it suitable for course use or independent study.\u003c\/p\u003e\u003cp\u003eThose seeking a casual or elementary overview of group theory for recreational use should look elsewhere; the material assumes mathematical maturity and is focused on profinite and residually finite contexts rather than elementary finite group theory.\u003c\/p\u003e\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eComprehensive, self-contained treatment that supports independent study.\u003c\/li\u003e\n\u003cli\u003eStrong emphasis on free profinite groups and subgroup structure useful for constructive work.\u003c\/li\u003e\n\u003cli\u003eIncludes homology and cohomology with minimal prerequisites, widening accessibility.\u003c\/li\u003e\n\u003cli\u003eNew appendices expand and update the theory, increasing the book's long-term value.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eMaterial assumes a level of mathematical maturity that may be challenging for beginners.\u003c\/li\u003e\n\u003cli\u003eFocused specialty content means it is not a general introduction to all group theory topics.\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\u003eProfinite Groups\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, 40\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthors\u003c\/td\u003e\n\u003ctd\u003eLuis Ribes, Pavel Zalesskii\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eEdition\u003c\/td\u003e\n\u003ctd\u003eSecond edition (contains three new appendices)\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePrimary topics\u003c\/td\u003e\n\u003ctd\u003eProfinite groups, free profinite groups, homology, cohomology, Galois groups\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIntended audience\u003c\/td\u003e\n\u003ctd\u003eGraduate students and specialists in algebra and number theory\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\u003ch2\u003eOur Verdict\u003c\/h2\u003e\u003cp\u003eProfinite Groups is a well-crafted, authoritative introduction and reference that rewards readers with the right background. It is good value for graduate students and researchers who need both foundational coverage and detailed treatments of free constructions and cohomological methods. Those seeking a light survey should consider a more elementary text, but for its scope this volume stands as a durable resource.\u003c\/p\u003e\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003eDoes this book require prior group theory experience?\u003c\/strong\u003e\u003cbr\u003eYes. It assumes mathematical maturity and familiarity with basic group theory and algebra at the undergraduate level.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eIs there new material in this edition?\u003c\/strong\u003e\u003cbr\u003eYes. The second edition adds three appendices, including a new characterization of free profinite groups.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eIs homology covered in depth?\u003c\/strong\u003e\u003cbr\u003eThe book describes homology and cohomology with minimal prerequisites, enough to apply these methods to profinite groups without extensive background texts.\u003c\/p\u003e","brand":"Luis Ribes, Pavel Zalesskii","offers":[{"title":"Default Title","offer_id":48191167922395,"sku":"3642262651","price":163.86,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/51ggn9m8LsL._SL1246.jpg?v=1769520432","url":"https:\/\/gearmusthave.com\/products\/profinite-groups-authoritative-introduction-and-reference","provider":"GearMustHave","version":"1.0","type":"link"}