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of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place.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 this book has minimal prerequisites and could be used as a text for an intermediate level graduate course; parts II and III are aimed at specialists in finite groups.
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Editorial Reviews
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"...Aschbacher's excellent book is required for all with specific interest in finite simple groups, but those with a less direct connection will also find much of value. In particular, they will filnd the only available collected treatment of Fischer's classification of 3-transposition groups, one of the most important and historic results from the theory of finite simple groups, presented lucidly by one of the most original minds in that area." Bulletin of the American Mathematical Society
Book Description
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.
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First Sentence:
Around 1970 Bernd Fischer proved his beautiful theorem classifying almost simple finite groups generated by 3-transpositions, and in the process discovered three new sporadic simple groups, now termed Fischer groups. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fischer's Theorem, Sylow's Theorem, Witt's Lemma, Marshall Hall, Therefore Theorem New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Around 1970 Bernd Fischer proved his beautiful theorem classifying almost simple finite groups generated by 3-transpositions, and in the process discovered three new sporadic simple groups, now termed Fischer groups. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fischer's Theorem, Sylow's Theorem, Witt's Lemma, Marshall Hall, Therefore Theorem New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 2
books:
- Finite Group Theory (Cambridge Studies in Advanced Mathematics) by M. Aschbacher in Back Matter
- Sporadic Groups (Cambridge Tracts in Mathematics) by Michael Aschbacher in Back Matter
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