The Classification Of The Finite Simple Groups, Number 2 (mathematical Surveys And Monographs)
by Daniel Gorenstein /
1995 / English / PDF
24.2 MB Download
The Classification Theorem is one of the main achievements of 20th
century mathematics, but its proof has not yet been completely
extricated from the journal literature in which it first appeared.
This is the second volume in a series devoted to the presentation
of a reorganized and simplified proof of the classification of the
finite simple groups. The authors present (with either proof or
reference to a proof) those theorems of abstract finite group
theory, which are fundamental to the analysis in later volumes in
the series. This volume provides a relatively concise and readable
access to the key ideas and theorems underlying the study of finite
simple groups and their important subgroups. The sections on
semisimple subgroups and subgroups of parabolic type give detailed
treatments of these important subgroups, including some results not
available until now or available only in journal literature. The
signalizer section provides an extensive development of both the
Bender Method and the Signalizer Functor Method, which play a
central role in the proof of the Classification Theorem. This book
would be a valuable companion text for a graduate group theory
course.
The Classification Theorem is one of the main achievements of 20th
century mathematics, but its proof has not yet been completely
extricated from the journal literature in which it first appeared.
This is the second volume in a series devoted to the presentation
of a reorganized and simplified proof of the classification of the
finite simple groups. The authors present (with either proof or
reference to a proof) those theorems of abstract finite group
theory, which are fundamental to the analysis in later volumes in
the series. This volume provides a relatively concise and readable
access to the key ideas and theorems underlying the study of finite
simple groups and their important subgroups. The sections on
semisimple subgroups and subgroups of parabolic type give detailed
treatments of these important subgroups, including some results not
available until now or available only in journal literature. The
signalizer section provides an extensive development of both the
Bender Method and the Signalizer Functor Method, which play a
central role in the proof of the Classification Theorem. This book
would be a valuable companion text for a graduate group theory
course.