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Matthew C. B. Zaremsky

  1. Rational homological stability for groups of partially symmetric automorphisms of free groups.

    Пт, 03/23/2012 - 15:01 — SomNambul
    Authors: Matthew C. B. Zaremsky
    Subjects: Group Theory
    Abstract

    Let F_{n+m} be the free group of rank n+m, with generating set
    S=\{x_1,...,x_{n+m}\}. An automorphism \phi of F_{n+m}$ is called partially
    symmetric if for each 1\leq i\leq m, \phi(x_i) is conjugate to x_j or x_j^{-1}
    for some 1\leq j\leq m. Let \Sigma Aut_n^m$ be the group of partially symmetric
    automorphisms.

  2. Strongly and Weyl transitive group actions on buildings arising from Chevalley groups.

    Пт, 01/07/2011 - 16:01 — SomNambul
    Authors: Peter Abramenko, Matthew C. B. Zaremsky
    Subjects: Group Theory
    Abstract

    Let K be a field and g(K) a Chevalley group (scheme) over K. Let (B,N) be the
    standard spherical BN-pair in g(K), with T=B\cap N and Weyl group W=N/T. We
    prove that there exist non-trivial elements w\in W such that all
    representatives of w in N have finite order. This allows us to exhibit examples
    of subgroups of g(Q_p) that act Weyl transitively but not strongly transitively
    on the affine building Delta associated with g(Q_p). Such examples were
    previously known only in the case when g(Q_p)=SL_2(Q_p) and Delta is a tree.

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