3-Transposition Groups [Paperback]

Contains the first complete published proof of Fischer's Theorem on the classification of 3-transposition groups.The theory of 3-transposition groups has become an important part of finite simple group theory. 3-Transposition Groups contains the first published proof of the fundamental Fischer's Theorem on the classification of 3-transposition groups, written out completely in one place. Part I has minimal prerequisites and can be used as a text for an intermediate level graduate course on finite groups. Parts II and III are aimed at specialists in finite groups and are a step in the author's program (begun in his earlier book, Sporadic Groups) to supply a strong foundation for the theory of sporadic groups.The theory of 3-transposition groups has become an important part of finite simple group theory. 3-Transposition Groups contains the first published proof of the fundamental Fischer's Theorem on the classification of 3-transposition groups, written out completely in one place. Part I has minimal prerequisites and can be used as a text for an intermediate level graduate course on finite groups. Parts II and III are aimed at specialists in finite groups and are a step in the author's program (begun in his earlier book, Sporadic Groups) to supply a strong foundation for the theory of sporadic groups.In 1970 Bernd Fischer proved his beautiful theorem classifying the almost simple groups generated by 3-transpositions, and in the process discovered three new sporadic groups, now known as the Fischer groups. Since then, the theory of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place. Fischer's result, while important and deep (covering a number of complex examples), can be understood by any student with some knowledge of elementary group theory and finite geometry. Part I of tl£0