Generix never gives up

2006 ◽  
Vol 71 (2) ◽  
pp. 599-610 ◽  
Author(s):  
Eric Jaligot
Keyword(s):  
Morley Rank ◽  
Carter Subgroup ◽  
Minimal Counterexample ◽  
Finite Morley Rank

AbstractWe prove conjugacy and generic disjointness of generous Carter subgroups in groups of finite Morley rank. We elaborate on groups with a generous Carter subgroup and on a minimal counterexample to the Genericity Conjecture.

scholarly journals CONJUGACY OF CARTER SUBGROUPS IN GROUPS OF FINITE MORLEY RANK

2008 ◽  
Vol 08 (01) ◽  
pp. 41-92 ◽  
Author(s):  
OLIVIER FRÉCON
Keyword(s):  
Conjugacy Class ◽  
Algebraic Groups ◽  
Simple Groups ◽  
Morley Rank ◽  
Minimal Counterexample ◽  
Finite Morley Rank ◽  
Cartan Subgroups

The Cherlin–Zil'ber Conjecture states that all simple groups of finite Morley rank are algebraic. We prove that any minimal counterexample to this conjecture has a unique conjugacy class of Carter subgroups, which are analogous to Cartan subgroups in algebraic groups.

Sous-groupes de Carter dans les groupes de rang de Morley fini

2004 ◽  
Vol 69 (1) ◽  
pp. 23-33
Author(s):  
Olivier Frécon
Keyword(s):  
Conjugacy Class ◽  
Solvable Group ◽  
Closed Subgroup ◽  
Nilpotent Subgroup ◽  
Morley Rank ◽  
Carter Subgroup ◽  
Locally Nilpotent ◽  
Finite Morley Rank

RésuméA Carter subgroup is a self-normalizing locally nilpotent subgroup. For studying these subgroups in groups of finite Morley rank, we introduce the new notion of a locally closed subgroup. We show that every solvable group of finite Morley rank has a unique conjugacy class of Carter subgroups.

scholarly journals On Groups of Finite Morley Rank with Weakly Embedded Subgroups

1999 ◽  
Vol 211 (2) ◽  
pp. 409-456 ◽  
Author(s):  
Tuna Altınel ◽  
Alexandre Borovik ◽  
Gregory Cherlin
Keyword(s):  
Morley Rank ◽  
Finite Morley Rank

scholarly journals Lascar and Morley ranks differ in differentially closed fields

1999 ◽  
Vol 64 (3) ◽  
pp. 1280-1284 ◽  
Author(s):  
Ehud Hrushovski ◽  
Thomas Scanlon
Keyword(s):  
Fundamental Issue ◽  
Morley Rank ◽  
Closed Fields ◽  
The Family ◽  
Finite Morley Rank

We note here, in answer to a question of Poizat, that the Morley and Lascar ranks need not coincide in differentially closed fields. We will approach this through the (perhaps) more fundamental issue of the variation of Morley rank in families. We will be interested here only in sets of finite Morley rank. Section 1 consists of some general lemmas relating the above issues. Section 2 points out a family of sets of finite Morley rank, whose Morley rank exhibits discontinuous upward jumps. To make the base of the family itself have finite Morley rank, we use a theorem of Buium.

scholarly journals Signalizers and balance in groups of finite Morley rank

2009 ◽  
Vol 321 (5) ◽  
pp. 1383-1406 ◽  
Author(s):  
Jeffrey Burdges
Keyword(s):  
Morley Rank ◽  
Finite Morley Rank

scholarly journals Tame minimal simple groups of finite Morley rank

2004 ◽  
Vol 276 (1) ◽  
pp. 13-79 ◽  
Author(s):  
Gregory Cherlin ◽  
Eric Jaligot
Keyword(s):  
Simple Groups ◽  
Morley Rank ◽  
Finite Morley Rank

On CN-Groups of Finite Morley Rank

1994 ◽  
Vol 50 (3) ◽  
pp. 532-546 ◽  
Author(s):  
Mark DeBonis ◽  
Ali Nesin
Keyword(s):  
Morley Rank ◽  
Finite Morley Rank
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