23 research outputs found
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
Simple groups of Morley rank 5 are bad
By exploiting the geometry of involutions in -groups of finite
Morley rank, we show that any simple group of Morley rank is a bad group
all of whose proper definable connected subgroups are nilpotent of rank at most
. The main result is then used to catalog the nonsoluble connected groups of
Morley rank
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Moufang sets of finite Morley rank
We study proper Moufang sets of finite Morley rank for which either the root groups are abelian or the roots groups have no involutions and the Hua subgroup is nilpotent. We give conditions ensuring that the little projective group of such a Moufang set is isomorphic to PSL2(F) for F an algebraically closed field. In particular, we show that any infinite quasisimple L*-group of finite Morley rank of odd type for which (B;N;U) is a split BN-pair of Tits rank 1 is isomorphic to SL2(F) or PSL2(F) provided that U is abelian. Additionally, we show that same conclusion can reached by replacing the hypothesis that U be abelian with the hypotheses that the intersection of B and N is nilpotent and U is definable and without involutions. As such, we make progress on the open problem of determining the simple groups of finite Morley rank with a split BN-pair of Tits rank 1, a problem tied to the current attempt to classify all simple groups of finite Morley rank
High Surface Area and Z′ in a Thermally Stable 8-fold Polycatenated Hydrogen-bonded Framework
1,3,5-Tris(4-carboxyphenyl)benzene assembles into an intricate 8-fold polycatenated assembly of (6,3) hexagonal nets formed through hydrogen bonds and π-stacking. One polymorph features 56 independent molecules in the asymmetric unit, the largest Z′ reported to date. The framework is permanently porous, with a BET surface area of 1095 m2 g−1 and readily adsorbs N2, H2 and CO2
Generically n-transitive permutation groups
Non UBCUnreviewedAuthor affiliation: Universität MünsterPostdoctora
Actions of on groups of finite Morley rank without involutions
We investigate faithful representations of as
automorphisms of a connected group of finite Morley rank. We target a lower
bound of on the rank of such a nonsolvable , and our main result
achieves this in the case when is without involutions. In the course of our
analysis, we also prove a corresponding bound for solvable by leveraging
recent results on the abelian case. We conclude with an application towards
establishing natural limits to the degree of generic transitivity for
permutation groups of finite Morley rank