{"product_id":"generators-and-relations-for-discrete-groups-classic-reference","title":"Generators and Relations for Discrete Groups - Classic Reference","description":"\u003cp\u003eIn this review of Generators and Relations for Discrete Groups the bottom line is clear: this is a specialist reference for mathematicians and advanced students who need a compact catalogue of abstract definitions and small-order group data. The reviewer finds the book most valuable for its curated tables and focused scope rather than as an introductory textbook. It is concise, historically grounded, and best used as a supplementary reference when working with permutation groups, congruent transformation groups, or reflection-generated groups in Euclidean space.\u003c\/p\u003e\n\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n \u003cli\u003e\n\u003cstrong\u003eCurated tables:\u003c\/strong\u003e The book includes tables covering low-order groups and specific classes that save time when searching for concrete examples and presentations.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eCoverage of permutation groups:\u003c\/strong\u003e It addresses permutation groups of small degree and points readers to classical tables for exhaustive listings.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eReflection groups:\u003c\/strong\u003e Groups generated by reflections in real Euclidean space are treated, which aids work on symmetry and geometric group theory.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eLinear fractional and symmetric groups:\u003c\/strong\u003e The text presents definitions and material on linear fractional, symmetric, and alternating groups useful for algebraic classification tasks.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eFinite and infinite congruent transformation groups:\u003c\/strong\u003e The reviewer notes useful entries on both finite and infinite groups arising from congruent transformations.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eConcise editorial approach:\u003c\/strong\u003e The authors restrict scope deliberately to keep the work manageable and focused for practical reference use.\u003c\/li\u003e\n\u003c\/ul\u003e\n\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis work is aimed at researchers, graduate students, and instructors in pure mathematics who need a compact reference for group presentations and low-order group data. It is particularly handy for those working in algebraic or geometric group theory who require quick access to definitions and tables for permutation and reflection-generated groups.\u003c\/p\u003e\n\n\u003cp\u003eIt is less suitable as a first course textbook for beginners: readers seeking extensive pedagogical exposition, worked exercises, or a broad survey of all finitely generated groups should look elsewhere. The book assumes some familiarity with group-theoretic language and classical references.\u003c\/p\u003e\n\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n \u003cli\u003eConcise tables provide immediate reference for low-order and classical groups.\u003c\/li\u003e\n \u003cli\u003eUseful treatment of reflection-generated groups for geometric applications.\u003c\/li\u003e\n \u003cli\u003eCompact focus makes it easy to consult specific group definitions without excessive background material.\u003c\/li\u003e\n \u003cli\u003eIncludes material on symmetric, alternating, and linear fractional groups, aiding classification tasks.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n \u003cli\u003eNot intended as an introductory textbook; readers new to group theory may find it terse.\u003c\/li\u003e\n \u003cli\u003eScope is deliberately limited, so it does not catalog every conceivable finitely generated group.\u003c\/li\u003e\n\u003c\/ul\u003e\n\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n \u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eGenerators and Relations for Discrete 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. 1. Folge, 14\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eAuthors\u003c\/td\u003e\n\u003ctd\u003eHarold Scott Macdonald Coxeter, William O. J. Moser\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eMain focus\u003c\/td\u003e\n\u003ctd\u003eTables and definitions for finitely generated and low-order groups\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eNotable content\u003c\/td\u003e\n\u003ctd\u003ePermutation groups, reflection groups, linear fractional groups\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eIntended audience\u003c\/td\u003e\n\u003ctd\u003eResearchers and advanced students in pure mathematics\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eGenerators and Relations for Discrete Groups is a focused, practical reference that rewards readers who already know group-theoretic basics. It delivers compact, well-organized tables and concise treatments of reflection and permutation groups, making it good value for specialists who need reliable, quick access to classical group presentations.\u003c\/p\u003e\n\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes this book include tables for small permutation groups?\u003c\/strong\u003e\u003cbr\u003eYes, it contains tables and commentary on permutation groups of low degree and refers to classical exhaustive tables for degree up to 8.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eIs this suitable for undergraduate self-study?\u003c\/strong\u003e\u003cbr\u003eNot as a primary textbook; it is best used alongside more introductory texts because it is concise and assumes prior familiarity with group theory.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eAre geometric reflection groups covered?\u003c\/strong\u003e\u003cbr\u003eYes, groups generated by reflections in real Euclidean space are discussed and tabulated for various dimensions.\u003c\/p\u003e","brand":"Harold Scott Macdonald Coxeter, William O. 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