Groupes finis

This text is an extended version of the lecture notes for a course on representation theory of finite groups that was given by the authors during several years for graduate and postgraduate students of Novosibirsk State University and Sobolev Institute of Mathematics.

The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the theory over complex numbers which is Character Theory. A large number of worked-out examples are the main feature of these notes. The prerequisite for this note is basic group theory and linear algebra.

This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.

Notes used for a course held in 2016 in the School of Advances in Group Theory and Applications, for some lectures given in 2018 for the students of the Master in Mathematics of the Vrije Universiteit Brussels, a course for master and Ph.D. students at the Universidade de S\~ao Paulo and at the conference Group algebras, representations and computations. We revise some problems on the study of finite subgroups of the group of units of integral group rings of finite groups and...

The article presents several methods for the arithmetic of finite abelian groups. We introduce a tool - already used by Delsarte in [1] as I found out later - analogous to Dirichlet's convolution to obtain combinatorial results on these groups. Using this convolution and some group actions, we deduce an interesting fact : the number of generating subsets of a finite abelian group is always a multiple of the order of the group. Eventually, we prove a theorem about the generati...

This is a book on Group.

This is a nearly complete manuscript left behind by Boris Weisfeiler before his disappearance during a hiking trip in Chile in 1985. It is posted on a request from the author's sister, Olga Weisfeiler.

This is a collection of open problems in group theory proposed by hundreds of mathematicians from all over the world. It has been published every 2--4 years since 1965. This is the 20th edition, which contains 126 new problems and a number of comments on problems from the previous editions.

Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).

In this article we present an extensive survey on the developments in the theory of non-abelian finite groups with abelian automorphism groups, and pose some problems and further research directions.