Construction of Curtis-Phan-Tits system in black box classical groups

We present a polynomial time Monte-Carlo algorithm for finite simple black box classical groups of odd characteristic which constructs all root ${\rm{SL}}_2(q)$-subgroups associated with the nodes of the extended Dynkin diagram of the corresponding algebraic group.Comment: 35 page

Black box groups

We propose a uniform approach for recognizing all black box groups of Lie type which is based on the analysis of the structure of the centralizers of involutions. Our approach can be viewed as a computational version of the classification of the finite simple groups. We present an algorithm which constructs a long root SL2(q)-subgroup in a finite simple group of Lie type of odd characteristic, then we use the Aschbacher's "Classical Involution Theorem" as a model in the recognition algorithm and we construct all root SL2(q)-subgroups corresponding to the nodes in the extended Dynkin diagram, that is, we construct the extended Curtis - Phan - Tits system of the finite simple groups of Lie type of odd characteristic. In particular, we construct all subsystem subgroups which can be read from the extended Dynkin diagram. We also present an algorithm which determines whether the p-core (or "unipotent radical") O-p(G) of a black box group G is trivial or not, where G/O-p(G) is a finite simple classical group of odd characteristic p, answering a well-known question of Babai and Shalev

Black box groups

We propose a uniform approach for recognizing all black box groups of Lie type which is based on the analysis of the structure of the centralizers of involutions. Our approach can be viewed as a computational version of the classification of the finite simple groups. We present an algorithm which constructs a long root SL2(q)-subgroup in a finite simple group of Lie type of odd characteristic, then we use the Aschbacher's "Classical Involution Theorem" as a model in the recognition algorithm and we construct all root SL2(q)-subgroups corresponding to the nodes in the extended Dynkin diagram, that is, we construct the extended Curtis - Phan - Tits system of the finite simple groups of Lie type of odd characteristic. In particular, we construct all subsystem subgroups which can be read from the extended Dynkin diagram. We also present an algorithm which determines whether the p-core (or "unipotent radical") O-p(G) of a black box group G is trivial or not, where G/O-p(G) is a finite simple classical group of odd characteristic p, answering a well-known question of Babai and Shalev

Generation of finite classical groups by pairs of elements with large fixed point spaces

We study 'good elements' in finite 2n-dimensional classical groups G: namely t is a 'good element' if o(t) is divisible by a primitive prime divisor of q(n) 1 for the relevant field order q, and t fixes pointwise an n-space. The group SL2n(q) contains such elements, and they are present in SU2n, (q), Sp(2n)(q),SO2n is an element of&(q), only if n is odd, even, even, respectively. We prove that there is an absolute positive constant c such that two random conjugates of t generate G with probability at least c, if G not equal SO2n is an element of (2) and G Sp(2n)(q) with q even. In the exceptional case G = Sp(2n)(q) with q even, two conjugates of t never generate G: in this case we prove that two random conjugates of t generate a subgroup SO2n is an element of(q) with probability at least c. The results underpin analysis of new constructive recognition algorithms for classical groups in even characteristic, which succeed where methods utilising involution centralisers are not available. (C) 2014 Elsevier Inc. All rights reserved

Renovascular hypertension in childhood: A nation-wide survey

43rd ERA-EDTA Congress -- JUL 15-18, 2006 -- Glasgow, SCOTLANDWOS: 000239919002224…ERA, EDT

Mitochondrial carrier homolog 1 (Mtch1) antibodies in neuro-Behcet's disease

Efforts for the identification of diagnostic autoantibodies for neuro-Behcet's disease (NBD) have failed. Screening of NBD patients' sera with protein macroarray identified mitochondrial carrier homolog 1 (Mtch1), an apoptosis-related protein, as a potential autoantigen. ELISA studies showed serum Mtch1 antibodies in 68 of 144 BD patients with or without neurological involvement and in 4 of 168 controls corresponding to a sensitivity of 47.2% and specificity of 97.6%. Mtch1 antibody positive NBD patients had more attacks, increased disability and lower serum nucleosome levels. Mtch1 antibody might be involved in pathogenic mechanisms of NBD rather than being a coincidental byproduct of autoinflammation. (C) 2013 Elsevier B.V. All rights reserved