20 research outputs found

    Covering certain Wreath Products with Proper Subgroups

    Full text link
    For a non-cyclic finite group XX let σ(X)\sigma(X) be the least number of proper subgroups of XX whose union is XX. Precise formulas or estimates are given for σ(S≀Cm)\sigma(S \wr C_{m}) for certain nonabelian finite simple groups SS where CmC_m is a cyclic group of order mm

    On the generating graph of a simple group

    Get PDF
    The authors were supported by Universita di Padova (Progetto di Ricerca di Ateneo: Invariable generation of groups). The second author was also supported by an Alexander von Humboldt Fellowship for Experienced Researchers, by OTKA grants K84233 and K115799, and by the MTA Renyi Lendulet Groups and Graphs Research Group.The generating graph Γ(H) of a finite group H is the graph defined on the elements of H, with an edge between two vertices if and only if they generate H. We show that if H is a sufficiently large simple group with Γ(G) ≅ Γ(H) for a finite group G, then G ≅ H. We also prove that the generating graph of a symmetric group determines the group.PostprintPeer reviewe
    corecore