School of Mathematics & Physics, University of Lincoln
Prof. E. Khukhro will continue his minicourse. Further lectures will develop the material in the first talk, giving more explanations and examples.
LECTURE 2: 06/10 (segunda-feira): “Associated Lie rings of nilpotent groups”
The construction of the associated Lie ring of a nilpotent group will be described, its definition and basic properties. Examples of applications will be given. Advantages and shortcomings of this construction will be discussed.
LECTURE 3: 08/10 (quarta-feira): “Using Baker–Campbell–Hausdorff formula in the study of nilpotent $p$-groups”.
Initially, the Baker–Campbell–Hausdorff formula was primarily a basis for the EXP and LOG functors in the study of Lie groups. Its applications to finite groups are not possible in general, yet there are some successful application in certain special cases. Definition and basic properties of the Mal’cev and Lazard correspondences will be described. Examples of applications will be given. Advantages and shortcomings of this construction will be discussed.