In this talk we will present recent results about fixed points of automorphisms in locally finite groups. Let pbe a prime and G a locally finite group containing an elementary abelian psubgroup A of rank at least 3 such that C_{G }(A) is Chernikov and C_{G }(a) involves no infinite simple groups for any a ∈ A^{#}. We show that G is almost locally soluble. To prove this result, we first give a characterization of PSL_{p }(k). Theorem. [1] An infinite simple locally finite group G admits an elementary abelian pgroup of automorphisms A such that C_{G }(A) is Chernikov and C_{G }(a) involves no infinite simple groups for any a ∈ A^{# }if and only if G is isomorphic to PSL_{p }(k) for some locally finite field k of characteristic different from p and A has order <nobr> p^{2}. This is a joint work with Mahmut Kuzucuoglu and Pavel Shumyatsky.
[1] Ersoy, K., Kuzucuoglu, M., Shumyatsky, P., Locally finite groups and their subgroups with small centralizers, J. Algebra, Vol. 481, 1 July 2017, p.111. ρ
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27 entries found
 April

27. April17:00  18:00
Location: 48436Algebra, Geometry and Computer AlgebraKivanv Ersoy, TU Kaiserslautern: Locally finite groups with small centralizers
 March

08. March17:00  18:00
Location: 48436AG Algebra, Geometrie und Computer AlgebraMichael Geline, Northern Illinois University: Some quantitative and qualitative aspects of Knörr lattices
These lattices are the <nobr></nobr> padic representations of finite groups whose invertible endomorphisms can be distinguished by the trace function. They include the absolutely irreducible lattices as well as the indecomposable lattices of rank not divisible by p. Knörr introduced them in a 1988 paper in connection with Brauer's height zero conjecture. They are now known also to be connected with Alperin's weight conjecture. I will explain this in the talk, and, time permitting, also give a quantitative result: Knörr lattices for the elementary abelian group of order 8, over an dvr unramified over the 2adics, do not exist.
 February

23. February16:00  17:00
Location: 48436AG Algebra, Geometrie und Computer AlgebraProf. Dr. Eugenii Shustin, Tel Aviv University; Real morsifications of plane curve singularities.
A real morsification of a real plane curve singularity is a real deformation with the maximal possible number of hyperbolic nodes (i.e., equivalent to x^{2}y^{2}=0 over R). We prove that any real plane curve singularity admits a real morsification. This was known before only in the case of all local branches being real (A'Campo, GusseinZade). We also discuss a relation between real morsifications and the topology of singularities and extend to arbitrary real morsifications the BalkeKaenders theorem stating that the A'CampoGusseinZade diagram associated to the morsification uniquely determines the real topological type of the initial curve singularity. Joint work with Piter Leviant.

09. February17:00  18:00
Location: 48436AG Algebra, Geometrie und Computer AlgebraCharles Eaton, University of Manchester: Loewy length of blocks
I will give a brief survey on results and conjectures about the Loewy length of a block of a finite group. This includes work with Michael Livesey giving precise upper and lower bounds for 2blocks with abelian defect groups.

06. February15:30  17:00
Location: 48438AG Algebra, Geometrie und Computer AlgebraMagdalena Boos, RuhrUniversität Bochum: Using quiver representations to prove finiteness criteria
 January

26. January16:00  17:00
Location: 48436AG Algebra, Geometrie und Computer AlgebraProf. Dr. Alexander Tikhomirov, HSE Moscow, z.Z. MPIM Bonn: On the moduli spaces of stable rank two coherent sheaves on projecti
Vortrag zum jetzigen Kenntnisstand über Modulräume
von Vektorbündeln und Garben auf dem projektiven Raum. 
19. January17:00  18:00
Location: 48436AG Algebra, Geometrie und Computer AlgebraIris Köster, Universität Stuttgart: Sylow Numbers in Character Tables and Integral Group Rings
The Sylow pnumber of a finite group is defined as the number of Sylow psubgroups of the given group. In this talk we want to consider a question of G. Navarro whether character tables determine the Sylow numbers of the underlying group. In the second part of the talk we analyze the question whether the integral group rings determines the Sylow numbers.