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Alireza Abdollahi

  1. Engel Elements in Groups.

    Tue, 02/02/2010 - 16:01 — SomNambul
    Authors: Alireza Abdollahi
    Subjects: Group Theory
    Abstract

    We give a survey of results on the structure of right and left Engel elements
    of a group. We also present some new results in this topic.

  2. Powerful $p$-groups have noninner automorphisms of order $p$ and some cohomology.

    Mon, 11/16/2009 - 16:01 — SomNambul
    Authors: Alireza Abdollahi
    Subjects: Group Theory
    Abstract

    In this paper we study the longstanding conjecture of whether there exists a
    noninner automorphism of order $p$ for a finite non-abelian $p$-group. We prove
    that if $G$ is a finite non-abelian $p$-group such that $G/Z(G)$ is powerful
    then $G$ has a noninner automorphism of order $p$ leaving either $\Phi(G)$ or
    $\Omega_1(Z(G))$ elementwise fixed.

  3. Non-nilpotent graph of a group.

    Fri, 10/02/2009 - 09:41 — SomNambul
    Authors: Alireza Abdollahi, Mohammad Zarrin
    Subjects: Group Theory
    Abstract

    We associate a graph $\mathcal{N}_{G}$ with a group

  4. Determinants of adjacency matrices of graphs.

    Tue, 08/25/2009 - 22:41 — SomNambul
    Authors: Alireza Abdollahi
    Subjects: Combinatorics
    Abstract

    We study the set of all determinants of adjacency matrices of graphs with a
    given number of vertices.

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