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Sukru Yalcinkaya

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

    Wed, 08/18/2010 - 15:01 — SomNambul
    Authors: Sukru Yalcinkaya, Alexandre Borovik
    Subjects: Group Theory
    Abstract

    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.

  2. Construction of long root SL(2,q)-subgroups in black box groups.

    Wed, 01/20/2010 - 16:01 — SomNambul
    Authors: Sukru Yalcinkaya
    Subjects: Group Theory
    Abstract

    We present a one sided Monte--Carlo algorithm which constructs a long root
    $\sl_2(q)$-subgroup in $X/O_p(X)$, where $X$ is a black-box group and
    $X/O_p(X)$ is a finite simple group of Lie type defined over a field of odd
    order $q=p^k > 3$ for some $k\geqslant 1$. Our algorithm is based on the
    analysis of the structure of centralizers of involutions and can be viewed as a
    computational version of Aschbacher's Classical Involution Theorem.

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