Sylow theory for p = 0 in solvable groups of finite Morley rank

Sylow theory for p = 0 in solvable groups of finite Morley rank Abstract The algebraicity conjecture for simple groups of finite Morley rank, also known as the Cherlin–Zil'ber conjecture, states that simple groups of finite Morley rank are simple algebraic groups over algebraically closed fields. In the last fifteen years, the main line of attack on this problem has been Borovik's program of transferring methods from finite group theory, which has led to considerable progress; however, the conjecture itself remains completely open. In Borovik's program, groups of finite Morley rank are divided into four types, odd, even, mixed, and degenerate, according to the structure of their Sylow 2-subgroup. For even and mixed type the algebraicity conjecture has been proven. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Group Theory de Gruyter

Sylow theory for p = 0 in solvable groups of finite Morley rank

Journal of Group Theory, Volume 9 (4) – Jul 1, 2006

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Publisher
de Gruyter
Copyright
Copyright © 2006 by the
ISSN
1433-5883
eISSN
1435-4446
DOI
10.1515/JGT.2006.030
Publisher site
See Article on Publisher Site

Abstract

Abstract The algebraicity conjecture for simple groups of finite Morley rank, also known as the Cherlin–Zil'ber conjecture, states that simple groups of finite Morley rank are simple algebraic groups over algebraically closed fields. In the last fifteen years, the main line of attack on this problem has been Borovik's program of transferring methods from finite group theory, which has led to considerable progress; however, the conjecture itself remains completely open. In Borovik's program, groups of finite Morley rank are divided into four types, odd, even, mixed, and degenerate, according to the structure of their Sylow 2-subgroup. For even and mixed type the algebraicity conjecture has been proven.

Journal

Journal of Group Theoryde Gruyter

Published: Jul 1, 2006

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