Items related to Abstract Root Subgroups and Simple Groups of Lie-Type...
Synopsis
It was already in 1964 [Fis66] when B. Fischer raised the question: Which finite groups can be generated by a conjugacy class D of involutions, the product of any two of which has order 1, 2 or 37 Such a class D he called a class of 3-tmnspositions of G. This question is quite natural, since the class of transpositions of a symmetric group possesses this property. Namely the order of the product (ij)(kl) is 1, 2 or 3 according as {i,j} n {k,l} consists of 2,0 or 1 element. In fact, if I{i,j} n {k,I}1 = 1 and j = k, then (ij)(kl) is the 3-cycle (ijl). After the preliminary papers [Fis66] and [Fis64] he succeeded in [Fis71J, [Fis69] to classify all finite "nearly" simple groups generated by such a class of 3-transpositions, thereby discovering three new finite simple groups called M(22), M(23) and M(24). But even more important than his classification theorem was the fact that he originated a new method in the study of finite groups, which is called "internal geometric analysis" by D. Gorenstein in his book: Finite Simple Groups, an Introduction to their Classification. In fact D. Gorenstein writes that this method can be regarded as second in importance for the classification of finite simple groups only to the local group-theoretic analysis created by J. Thompson.
"synopsis" may belong to another edition of this title.
Review
"The book is well written: the style is concise but not hard and most of the book is not too difficult to read for a graduate student. Some parts of it are certainly suited for a class."
--Mathematical Reviews
"About this title" may belong to another edition of this title.
Other Popular Editions of the Same Title
Search results for Abstract Root Subgroups and Simple Groups of Lie-Type...
Seller Image
Abstract Root Subgroups and Simple Groups of Lie-type
Seller: GreatBookPrices, Columbia, MD, U.S.A.
Seller rating 5 out of 5 stars
Condition: New. Seller Inventory # 21734081-n
Quantity: 15 available
Stock Image
Abstract Root Subgroups and Simple Groups of Lie-Type (Paperback)
Seller: Grand Eagle Retail, Mason, OH, U.S.A.
Seller rating 5 out of 5 stars
Paperback. Condition: new. Paperback. It was already in 1964 [Fis66] when B. Fischer raised the question: Which finite groups can be generated by a conjugacy class D of involutions, the product of any two of which has order 1, 2 or 37 Such a class D he called a class of 3-tmnspositions of G. This question is quite natural, since the class of transpositions of a symmetric group possesses this property. Namely the order of the product (ij)(kl) is 1, 2 or 3 according as {i,j} n {k,l} consists of 2,0 or 1 element. In fact, if I{i,j} n {k,I}1 = 1 and j = k, then (ij)(kl) is the 3-cycle (ijl). After the preliminary papers [Fis66] and [Fis64] he succeeded in [Fis71J, [Fis69] to classify all finite "nearly" simple groups generated by such a class of 3-transpositions, thereby discovering three new finite simple groups called M(22), M(23) and M(24). But even more important than his classification theorem was the fact that he originated a new method in the study of finite groups, which is called "internal geometric analysis" by D. Gorenstein in his book: Finite Simple Groups, an Introduction to their Classification. In fact D. Gorenstein writes that this method can be regarded as second in importance for the classification of finite simple groups only to the local group-theoretic analysis created by J. Thompson. After the preliminary papers [Fis66] and [Fis64] he succeeded in [Fis71J, [Fis69] to classify all finite "nearly" simple groups generated by such a class of 3-transpositions, thereby discovering three new finite simple groups called M(22), M(23) and M(24). Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9783034875967
Quantity: 1 available
Stock Image
Abstract Root Subgroups and Simple Groups of Lie-Type (Monographs in Mathematics)
Seller: Best Price, Torrance, CA, U.S.A.
Seller rating 5 out of 5 stars
Condition: New. SUPER FAST SHIPPING. Seller Inventory # 9783034875967
Quantity: 1 available
Stock Image
Abstract Root Subgroups and Simple Groups of Lie-Type (Monographs in Mathematics)
Seller: Lucky's Textbooks, Dallas, TX, U.S.A.
Seller rating 5 out of 5 stars
Condition: New. Seller Inventory # ABLING22Oct2817100391734
Quantity: Over 20 available
Seller Image
Abstract Root Subgroups and Simple Groups of Lie-type
Seller: GreatBookPrices, Columbia, MD, U.S.A.
Seller rating 5 out of 5 stars
Condition: As New. Unread book in perfect condition. Seller Inventory # 21734081
Quantity: 15 available
Stock Image
Abstract Root Subgroups and Simple Groups of Lie-Type (Monographs in Mathematics)
Seller: Ria Christie Collections, Uxbridge, United Kingdom
Seller rating 5 out of 5 stars
Condition: New. In. Seller Inventory # ria9783034875967_new
Quantity: Over 20 available
Seller Image
Abstract Root Subgroups and Simple Groups of Lie-Type
Published by
Birkhäuser Basel Jun 2012, 2012
ISBN 10: 3034875967
ISBN 13: 9783034875967
New
Taschenbuch
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. For finite groups, this theory has been developed in the 1970s mainly by M. Aschbacher, B. Fischer and the author. It was extended to arbitrary groups in the 1990s by the author. The theory of abstract root subgroups is an important tool to study and classify simple classical and Lie-type groups. 408 pp. Englisch. Seller Inventory # 9783034875967
Quantity: 2 available
Seller Image
Abstract Root Subgroups and Simple Groups of Lie-Type
Print on DemandSeller: moluna, Greven, Germany
Seller rating 4 out of 5 stars
Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. For finite groups, this theory has been developed in the 1970s mainly by M. Aschbacher, B. Seller Inventory # 4319155
Quantity: Over 20 available
Stock Image
Abstract Root Subgroups and Simple Groups of Lie-Type
Seller: Kennys Bookshop and Art Galleries Ltd., Galway, GY, Ireland
Seller rating 5 out of 5 stars
Condition: New. Series: Monographs in Mathematics. Num Pages: 402 pages, biography. BIC Classification: PBG. Category: (P) Professional & Vocational. Dimension: 244 x 170 x 21. Weight in Grams: 700. . 2012. Paperback. . . . . Seller Inventory # V9783034875967
Quantity: 15 available
Stock Image
Abstract Root Subgroups and Simple Groups of Lie-Type
Seller: Kennys Bookstore, Olney, MD, U.S.A.
Seller rating 5 out of 5 stars
Condition: New. Series: Monographs in Mathematics. Num Pages: 402 pages, biography. BIC Classification: PBG. Category: (P) Professional & Vocational. Dimension: 244 x 170 x 21. Weight in Grams: 700. . 2012. Paperback. . . . . Books ship from the US and Ireland. Seller Inventory # V9783034875967
Quantity: 15 available