25,059 research outputs found
Teoremas análogos de grupos finitos en grupos de rango de morley finito
Un método usado en grupos finitos para deducir, entre otros, los teoremas de reemplazo de Thompson y Timmesfeld [4], se desarrolla en versión de grupos de rango de Morley finito obteniéndose resultados análogos, lo que permite evidenciar como el rango de Morley funciona como una dimensión en un grupo infinito.A method used in finite group theory to deduce, among others, Thomsomp's and Timmesfeld's replacement theorems [4], is now developed in the context of groups of finite Morley rank and analogues results are obtained. This procedure then, allows to have an evidence on how the Morley rank behaves as a dimension for an infinite group
Involutive automorphisms of groups of finite Morley rank
We classify a large class of small groups of finite Morley rank:
-groups which are the infinite analogues of Thompson's
-groups. More precisely, we constrain the -structure of groups of finite
Morley rank containing a definable, normal, non-soluble,
-subgroup
Moufang sets of finite Morley rank of odd type
We show that for a wide class of groups of finite Morley rank the presence of
a split -pair of Tits rank forces the group to be of the form
and the -pair to be standard. Our approach is via
the theory of Moufang sets. Specifically, we investigate infinite and so-called
hereditarily proper Moufang sets of finite Morley rank in the case where the
little projective group has no infinite elementary abelian -subgroups and
show that all such Moufang sets are standard (and thus associated to
for an algebraically closed field of
characteristic not ) provided the Hua subgroups are nilpotent. Further, we
prove that the same conclusion can be reached whenever the Hua subgroups are
-groups and the root groups are not simple
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