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K. Bou-Rabee

  1. Asymptotic growth and least common multiples in groups.

    Thu, 01/28/2010 - 16:01 — SomNambul
    Authors: K. Bou-Rabee, D. B. McReynolds
    Subjects: Group Theory
    Abstract

    In this article we relate word and subgroup growth to certain functions that
    arise in the quantification of residual finiteness. One consequence of this
    endeavor is a pair of results that equate the nilpotency of a finitely
    generated group with the asymptotic behavior of these functions. The second
    half of this article investigates the asymptotic behavior of two of these
    functions. Our main result in this arena resolves a question of Bogopolski from
    the Kourovka notebook concerning lower bounds of one of these functions for
    nonabelian free groups.

  2. Bertrand's postulate and subgroup growth.

    Wed, 09/09/2009 - 22:08 — SomNambul
    Authors: K. Bou-Rabee, D. B. McReynolds
    Subjects: Group Theory
    Abstract

    In this article we investigate the L^1-norm of certain functions on groups
    called divisibility functions. Using these functions, their connection to
    residual finiteness, and integration theory on profinite groups, we define the
    residual average of a finitely generated group. One of the main results in this
    article is the finiteness of residual averages on finitely generated linear
    groups. Whether or not the residual average is finite depends on growth rates
    of indices of finite index subgroups.

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