Date: December 2nd 2014 Room: 2BC30 Time: 14:30 Speaker: Attila Maróti Institution: Technische Universität Kaiserslautern, Germany. Title: On finite linear group actions Abstract: This talk considers three related aspects of the situation when a finite group G acts irreducibly and faithfully on a finite vector space V. The first part of the talk is centered around the so-called non-coprime k(GV) problem. This is joint work with Robert M. Guralnick. The second part deals with the minimal size of a base for G. This is joint work with Zoltan Halasi. In the third part we will discuss some applications to Gluck's conjecture. This is joint work with James P. Cossey, Zoltan Halasi and Hung Ngoc Nguyen. ---------------- Date: December 3rd 2014 Room: 2BC30 Time: 14:30 Speaker: Martino Garonzi Institution: University of Padova, Italy. Title: Groups as squares of double cosets Abstract: I will present the content of a joint work with John Cannon, Dan Levy, Attila Maroti and Iulian Simion where we prove that any non-solvable finite group is the square of a double coset of a proper subgroup. As a consequence of this, any finite group which is not a cyclic p-group admits a factorization G = ABA where A,B are proper subgroups of G which can be taken to be conjugated if G is non-solvable. ---------------- Date: December 9th 2014 Room: 1A150 Time: 13:30 Speaker: Iulian Simion Institution: University of Padova, Italy. Title: Product coverings with unipotent Sylows Abstract: We discuss the problem of covering simple groups of Lie type by products of unipotent Sylows. The minimal number of such coverings is generically 4 but for certain particular families 3 can be attained. We show this in the context of groups with a sigma-setup. Similar coverings appear in different context in the literature. We mention the relevant results and some related problems. ----------------- Date: December 17th 2014 Room: 1BC45 Time: 11:30 Speaker: Mima Stanojkovski Institutions: University of Leiden, Netherlands and University of Padova, Italy. Title: Evolving groups and intensity Abstract: Let G be a finite group. We say that G is evolving if there are two nilpotent groups N and T of coprime orders such that G equals their semidirect product and every subgroup of N has a T -stable conjugate. It follows that nilpotent groups are evolving, but can we construct non-nilpotent examples? We will see how to build such groups starting from suitable pro-p-groups and looking at specific automorphisms of theirs. We will give as well a number theoretic interpretation of the problem.