A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

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

2011
*
Journal of Algebra
*

We study groups

doi:10.1016/j.jalgebra.2010.12.020
fatcat:glxlvvnd3jdotdmlvjc6o4kcn4
*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. ... 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 ... The author would also like to acknowledge Jeffrey Burdges and Alexandre Borovik for their assistance with a couple*of*points as well as the referee for many helpful suggestions. ...##
###
Page 8654 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

Van Maldeghem on classifying groups

*of**finite**Morley**rank*having some*BN*-*pair*. ... Math. 21 (1973), 1-57; ibid. 24 (1974), 191-239; MR 50 #7335] for*finite*groups with*split**BN*-*pair**of**rank*two to arbitrary groups without quoting this for the*finite*groups. ...##
###
Page 1420 of Mathematical Reviews Vol. , Issue 96c
[page]

1996
*
Mathematical Reviews
*

definable

*BN*-*pair**of*Tits*rank*at least three. ... Fields*of**finite**Morley**rank*are handled in Chapter 8. ...##
###
Simple groups of finite morley rank and Tits buildings

1999
*
Israel Journal of Mathematics
*

It follows that any infinite simple group

doi:10.1007/bf02775036
fatcat:sum5rojxm5hrjdyrvmfm5uzzeu
*of**finite**Morley**rank*with a spherical Moufang*BN*-*pair**of*Tits*rank*2 is either PSL3(K), PSp4(K ) or G2(K) for some algebraically closed field K. ... Using Theorem A we show THEOREM B: If G is an infinite simple group*of**finite**Morley**rank*with a spherical Moufang*BN*-*pair**of*Tits*rank*~ 2, then G is (interpretably) isomorphic to a simple algebraic group ... The paper was written while the first two authors were guests at the Institute*of*Mathematics*of*The Hebrew University*of*Jerusalem. ...##
###
Special abelian Moufang sets of finite Morley rank

2008
*
Journal of group theroy
*

Moufang sets are

doi:10.1515/jgt.2008.040
fatcat:qfgyyy44nfcihaucn7zf34opha
*split*doubly transitive permutation groups, or equivalently, groups with a*split**BN*-*pair**of**rank*one. ... In this paper, we study so-called special Moufang sets with abelian root groups, under the model-theoretic restriction that the groups have*finite**Morley**rank*. ... Acknowledgment This paper was written during a longer visit*of*the first author at the University*of*Bielefeld, supported by a travel grant from the Research Foundation in Flanders (Belgium) (F.W.O. ...##
###
Page 4190 of Mathematical Reviews Vol. , Issue 2000f
[page]

2000
*
Mathematical Reviews
*

In the paper under review the authors give a proof for the case

*of*a simple group with a*BN*-*pair**of*Tits*rank*at least 2 which is associated to a Moufang building. ...*finite**Morley**rank*and Tits buildings. ...##
###
Classification of Simple K*-Groups of Finite Morley Rank and Even Type: Geometric Aspects
[chapter]

2003
*
Groups, Combinatorics and Geometry
*

Generic groups can be handled either by constructing a

doi:10.1142/9789812564481_0001
fatcat:7yxre46d75euzbxlvaiue2d3se
*BN*-*pair*in G*of*(Tits)*rank*at least 3 [11] and the subsequent application*of*the classification*of**BN*-*pairs**of**finite**Morley**rank*(Kramer, van ... Identification We apply a very general result from [18, Theorem 3.14] : Fact 4 Let G * be an infinite simple group*of**finite**Morley**rank*with a spherical Moufang*BN*-*pair**of*Tits*rank*2. ...##
###
Moufang sets of finite Morley rank of odd type

2014
*
Journal of Algebra
*

We show that for a wide class

doi:10.1016/j.jalgebra.2014.01.001
fatcat:rsidk6hdzjcw5iqy66ep22zf5q
*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 PSL_2 and the*BN*-*pair*to be standard. ... 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 ... Acknowledgments The author would like to thank Katrin Tent and Tuna Altınel for several valuable suggestions and comments that lead to a refinement*of*both the content and the presentation*of*the paper ...##
###
Parabolic 2-local subgroups in groups of finite Morley rank of even type

2003
*
Journal of Algebra
*

Thus A is

doi:10.1016/s0021-8693(03)00393-4
fatcat:dtjznxjdi5fappq3jggeoab4my
*finite*and central in P . In particular [A, S] = 1. We claim that C(G, S) C(A). Then by the C(G, T )-theorem (Fact 16) and inspection*of*SL 2 (F ), we have A = 1, as claimed. ... We have P = N • (Q) with Q a nontrivial definable 2-subgroup*of*G. We suppose that P contains a Borel subgroup B*of*G and we set S = O 2 (B), which is connected by Fact 2. Let A = O 2 (P ). ... The point is that such extensions cannot have*finite**Morley**rank*. Fact 12 [*BN*, Theorem 8.4, p. 124] . ...##
###
Page 1885 of Mathematical Reviews Vol. , Issue 2004c
[page]

2004
*
Mathematical Reviews
*

Tits [Buildings

*of*spherical type and*finite**BN*-*pairs*, Lecture Notes in Math., 386, Springer, Berlin, 1974; MR 57 #9866]. ... This proves that there is no simple group*of**finite**Morley**rank**of*mixed type, provided the main conjecture is true for even type groups. ...##
###
Page 4557 of Mathematical Reviews Vol. , Issue 95h
[page]

1995
*
Mathematical Reviews
*

The article is a first step towards a classification

*of**BN*-*pairs**of**rank*| and*finite**Morley**rank*.*BN*-*pairs**of**rank*| are doubly transitive permutation groups. ... We say that a*finite*group is a rational group if its irreducible complex characters are all rational-valued. Suppose now that G is 4557 a*finit*Witt |*of*G. which subgr Amo! ...##
###
Special abelian Moufang sets of finite Morley rank in characteristic 2

2010
*
Journal of group theroy
*

In this paper we study special Moufang sets MðU; tÞ, with U abelian, under the additional restriction that they have

doi:10.1515/jgt.2009.031
fatcat:xqzimkniozdvhdsavw7drgwivi
*finite**Morley**rank*. ... endomorphisms*of*U centralize the Hua subgroup. ... It is shown in [10] that infinite simple groups*of**finite**Morley**rank*with such a*BN*-*pair**of*Tits*rank*at least 3 are indeed isomorphic to algebraic groups over algebraically closed fields. ...##
###
On small groups of finite Morley rank with a supertight automorphism
[article]

2022
*
arXiv
*
pre-print

We consider an infinite simple group

arXiv:2012.09582v3
fatcat:jlknslybmjaslbpts5satkfzmy
*of**finite**Morley**rank*G*of*Prüfer 2-*rank*1 which admits a supertight automorphism α such that the fixed-point subgroup C_G(α^n) is pseudofinite for all n∈ℕ∖{0}. ... In this set-up, we generalise the main theorem by dropping the assumption*of*the characteristic*of*the pseudofinite field F_1. We also correct a mistake from the earlier version. ... References 39 Acknowledgements We wish to thank Alexandre Borovik for bringing us together to work on this programme, for his encouragement and for his many helpful observations, especially related to*finite*...##
###
Page 6653 of Mathematical Reviews Vol. , Issue 2003i
[page]

2003
*
Mathematical Reviews
*

*Morley*

*rank*. ... Pedersen (Binghamton, NY) See also 20093, 55005, 57024, 81192. 20 GROUP THEORY AND GENERALIZATIONS 20A Foundations 2003i:20001 20A15 03C60 20E42 Tent, Katrin (D-WRZB-IM; Wiirzburg)

*Split*

*BN*-

*pairs*

*of*

*finite*...

##
###
Book Review: The classification of quasithin groups I, II

2005
*
Bulletin of the American Mathematical Society
*

These volumes, classifying the quasithin

doi:10.1090/s0273-0979-05-01071-2
fatcat:3rawrfnhszgnzguzvojkoub3xq
*finite*simple groups*of*even characteristic, are a major milestone in the history*of**finite*group theory. ... The classification*of**finite*simple groups*of*odd type occupied scores*of*group theorists during the 1960's and 1970's. ... By Bender's Strongly Embedded Theorem, if M contains N G (X) for every non-identity subgroup X*of*T , then G is a*split**BN*-*pair**of**rank*1, in particular, a known simple group. ...
« Previous

*Showing results 1 — 15 out of 94 results*