Results 1 to 10 of about 6,390 (190)
Finite group actions on abelian groups of finite Morley rank [PDF]
Model Theory, 2020 This paper develops some general results about actions of finite groups on (infinite) abelian groups in the finite Morley rank category. They are linked to a range of problems on groups of finite Morley rank.
A. Borovik
semanticscholar +7 more sources
Small groups of finite Morley rank with involutions [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2008 By analogy with Thompson's classification of nonsolvable finite N-groups, we classify groups of finite Morley rank with solvable local subgroups of even and of mixed type.
Adrien Deloro, E. Jaligot
semanticscholar +11 more sources
Weyl groups of small groups of finite Morley rank [PDF]
Israel Journal of Mathematics, 2009 We examine Weyl groups of minimal connected simple groups of finite Morley rank of degenerate type. We show that they are cyclic, and lift isomorphically to subgroups of the ambient group.
Jeffrey Burdges, Adrien Deloro
semanticscholar +9 more sources
Simple groups of finite Morley rank [PDF]
, 2008 The book gives a detailed presentation of the classification of the simple groups of finite Morley rank which contain a nontrivial unipotent 2-subgroup. They are linear algebraic groups over algebraically closed fields of characteristic 2. Although the story told in the book is inspired by the classification of the finite simple groups, it goes well ...
T. Altinel, A. Borovik, G. Cherlin
semanticscholar +4 more sources
Involutive automorphisms of $N_\circ^\circ$ groups of finite Morley rank [PDF]
, 2015 We classify a large class of small groups of finite Morley rank: $N_\circ^\circ$-groups which are the infinite analogues of Thompson's $N$-groups. More precisely, we constrain the $2$-structure of groups of finite Morley rank containing a definable ...
Adrien Deloro, E. Jaligot
semanticscholar +6 more sources
On analogies between algebraic groups and groups of finite Morley rank [PDF]
, 2008 We prove that in a connected group of finite Morley rank the centralizers of decent tori are connected. We then apply this result to the analysis of minimal connected simple groups of finite Morley rank.
T. Altinel, Jeffrey Burdges
semanticscholar +6 more sources
On solvable groups of finite Morley rank [PDF]
Transactions of the American Mathematical Society, 1990 We investigate solvable groups of finite Morley rank. We find conditions on G G for G ′ G’ to split in G G . In particular, if G ′ G’ is abelian and Z ( G ) = 1 Z(G) = 1 we prove that
Ali Nesin
semanticscholar +4 more sources
Semisimple torsion in Groups of finite Morley Rank [PDF]
Journal of Mathematical Logic, 2008 We prove several results about groups of finite Morley rank without unipotent p-torsion: p-torsion always occurs inside tori, Sylow p-subgroups are conjugate, and p is not the minimal prime divisor of our approximation to the "Weyl group".
Jeffrey Burdges, G. Cherlin
semanticscholar +7 more sources
Actions of Groups of Finite Morley Rank on Small Abelian Groups [PDF]
The Bulletin of Symbolic Logic, 2009 AbstractWe classify actions of groups of finite Morley rank on abelian groups of Morley rank 2: there are essentially two, namely the natural actions ofSL(V)andGL(V)withVa vector space of dimension 2. We also prove an identification theorem for the natural module of SL2in the finite Morley rank category.
Adrien Deloro
semanticscholar +7 more sources
Lie rank in groups of finite Morley rank with solvable local subgroups [PDF]
Journal of Algebra, 2013 We prove a general dichotomy theorem for groups of finite Morley rank with solvable local subgroups and of Pr\"ufer p-rank at least 2, leading either to some p-strong embedding, or to the Pr\"ufer p-rank being exactly ...
Adrien Deloro, Éric Jaligot
core +8 more sources