The non-coprime k(GV) problem
and generation of finite groups

Marie Curie Fellowship 239169, Attila Maróti

       

The Rényi Institute concluded contract negotiations with the European Community, the project started on May 1, 2009.

The main fields of research are the following.

• The non-coprime k(GV) problem and related questions.
• Generation of finite groups; generating graph.
• Covering problems for groups.

Some training and research activities of the researcher

• Finite Simple Groups and Algebraic Groups: Representations, Geometries and Applications Summer School in Berlin, Germany, September 2009
• Visiting University of Padova, Padova, Italy, December 2009
• Conference for the memory of Maria Silvia Lucido, University of Padova, Italy, invited speaker, March 2010
• Ischia Group Theory 2010, Ischia, Italy, invited speaker, April 2010
• Groups and Their Actions, Bedlewo, Poland, August 2010
• Visiting University of Bristol, Bristol, England, January 2011
• Visiting University of Brescia, Brescia, Italy, March 2011
• Finite Groups and Their Automorphism Groups, Istanbul, Turkey, invited speaker, June 2011
• Linear Groups and Group Representations: Classification Problems, Milan, Italy, invited speaker, July 2011

Papers

• Robert M. Guralnick and Attila Maróti. On the non-coprime k(GV) problem.
     In preparation.
• John R. Britnell and Attila Maróti. Normal coverings of GL(n,q).
     In preparation.
• Tom De Medts and Attila Maróti. Perfect numbers and finite groups.
     Submitted.
• Attila Maróti and M. Chiara Tamburini. A solution to a problem of Wiegold.
     Submitted.
• Attila Maróti and M. Chiara Tamburini. Lifting (2,k)-generators of linear groups.
     To appear in Ischia group theory 2010. Proceedings of the conference in group theory.
• Andrea Lucchini and Attila Maróti. Rings as the unions of proper subrings.
     To appear in Algebras and Representation Theory.
• Attila Maróti and M. Chiara Tamburini. Bounds for the probability of generating the symmetric and alternating groups.
     Archiv der Mathematik Vol. 96 (2011), 115-121.
• Robert M. Guralnick and Attila Maróti. Average dimension of fixed point spaces with applications.
     Advances in Mathematics Vol. 226 (2011), 298-308.
• László Héthelyi, Erzsébet Horváth, Thomas M. Keller and Attila Maróti. Groups with few conjugacy classes.
     Proceedings of the Edinburgh Mathematical Society (2011) Vol. 54, 1-8.
• Martino Garonzi and Attila Maróti. Covering certain wreath products with proper subgroups.
  Journal of Group Theory (2011) Vol. 14 Issue 1, 103-125.
• Thomas Breuer, Robert M. Guralnick, Andrea Lucchini, Attila Maróti and Gábor P. Nagy. Hamiltonian cycles in the generating graphs of finite groups.
     Bulletin of the London Mathematical Society Vol. 42 Part 4 (2010) 621-633.
• Petra E. Holmes and Attila Maróti. Pairwise generating and covering sporadic simple groups.
     Journal of Algebra Vol. 324 Issue 1 (2010) 25-35.
• Charles Lanski and Attila Maróti. Ring elements as sums of units.
     Central European Journal of Mathematics. Vol. 7. Number 3. (2009) 395--399.