20 research outputs found
Covering certain Wreath Products with Proper Subgroups
For a non-cyclic finite group let be the least number of
proper subgroups of whose union is . Precise formulas or estimates are
given for for certain nonabelian finite simple groups
where is a cyclic group of order
On the generating graph of a simple group
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