Special abelian Moufang sets of finite Morley rank in characteristic 2

Wiscons, Josh

doi:10.1515/jgt.2009.031

Cited by 2 publications

(3 citation statements)

References 14 publications

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“…They also prove that the conjecture holds in characteristic larger than 2 provided that the Hua subgroup has an infinite centralizer in End(U ). In characteristic 2 [Wis10] proves the same restricted version of the conjecture before calling upon the classification of the even type simple groups of finite Morley rank to establish the full statement. …”

Section: H Is Without Infinite Elementary Abelian P-subgroups or 2 mentioning

confidence: 80%

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On groups of finite Morley rank with a split BN-pair of rank 1

Wiscons

2011

Journal of Algebra

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We study groups of finite Morley rank with a split BN-pair of Tits rank 1 in the case where the normal complement to B ∩ N in B is infinite and abelian. For such groups, we give conditions ensuring that the standard action of G on the cosets of B is isomorphic to the natural action of PSL 2 (F ) on P 1 (F ) for F an algebraically closed field. In particular, we show that SL 2 (F ) and PSL 2 (F ) are the only infinite quasisimple L * -groups of finite Morley rank possessing a split BN-pair of Tits rank 1 where the normal complement to B ∩ N in B is infinite abelian. Our approach is through the theory of Moufang sets and is tied to work attempting to classify the abelian Moufang sets of finite Morley rank.

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Section: H Is Without Infinite Elementary Abelian P-subgroups or 2 mentioning

confidence: 80%

“…(See[DMT08,Wis10].) If M(U , τ ) is an infinite special abelian Moufang set of finite Morley rank, then M(U , τ ) ∼ = M(F ), for F an algebraically closed field, provided U has characteristic 0 or 2.We now refocus the condition from [DMT08] that the Hua subgroup has an infinite centralizer in End(U ).Lemma 3.5.…”

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confidence: 99%

On groups of finite Morley rank with a split BN-pair of rank 1

Wiscons

2011

Journal of Algebra

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“…It is conjectured that every infinite proper Moufang set with abelian root groups is of the form M(J) for some quadratic Jordan division algebra J. When considering the rather restrictive class of Moufang sets of finite Morley rank, this conjecture seems to have a positive answer, and here, all of the Moufang sets appear to arise, as expected, from a field, see [DMT08], [Wis10], [Wis11]. We now investigate if it is possible for Moufang sets of finite Morley rank to have nonabelian root groups.…”

Section: Introductionmentioning

confidence: 89%

Moufang sets of finite Morley rank of odd type

Wiscons

2014

Journal of Algebra

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We show that for a wide class of groups of finite Morley rank the presence of a split $BN$-pair of Tits rank $1$ forces the group to be of the form $\operatorname{PSL}_2$ and the $BN$-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 $2$-subgroups and show that all such Moufang sets are standard (and thus associated to $\operatorname{PSL}_2(F)$ for $F$ an algebraically closed field of characteristic not $2$) provided the Hua subgroups are nilpotent. Further, we prove that the same conclusion can be reached whenever the Hua subgroups are $L$-groups and the root groups are not simple

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Special abelian Moufang sets of finite Morley rank in characteristic 2

Cited by 2 publications

References 14 publications

On groups of finite Morley rank with a split BN-pair of rank 1

On groups of finite Morley rank with a split BN-pair of rank 1

Moufang sets of finite Morley rank of odd type

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