Groupes finis

Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this note, we give some characterizations for normality of H in G. As a consequence we get a very short and elementary proof of the Main Theorem of [5], which avoids the use of the classification of finite simple groups

These are the notes of some lectures given by the author for a workshop held at TIFR, Mumbai in December, 2011, giving an exposition of the Deligne-Lusztig theory.

Let $G$ be a finite group and $Ch_i(G)$ some quantitative sets. In this paper we study the influence of $Ch_i(G)$ to the structure of $G$. We present a survey of author and his colleagues' recent works.

In this note, we study the finite groups with the number of cylic subgroups no greater than 6.

These are the notes from an Oberwolfach Seminar which we ran from 23--29 May 2010.

This document is rather a course about groups than a research paper. However, it can be of interest for many master students in mathematics which are devoted to the p-group classification theory. This paper is inspirated of the course of David Clausen from the university of Puget Sound (USA) on the classification of groups of order 16. His publication was made on GNU Licence. However, his publication contained some typo errors which make difficult the understanding of his met...

These are partial lecture notes from the fifteen Ess\'en Lectures for graduate students at Uppsala University given (in four days!) in June 2013.

These informal notes are closely based on a series of eight lectures given by J.-P. Serre at the University of Oregon in October 1998. Professor Serre gave two talks per week for four weeks. The first talk each week was concerned with constructing embeddings of finite groups, especially $\PSL_2(p)$ and $\PGL_2(p)$, into Lie groups. The second talk each week was about generalizations of the notion of complete reducibility in group theory, especially in positive characteristi...

Arithmetical properties of a finite group are properties of the group which are defined by its arithmetical parameters such as the order of the group, the element orders and so on. In this paper, we discuss a number of results on arithmetical properties of finite groups and characterizations of finite groups by their arithmetical parameters obtained recently. This paper is based on the talk by the author given in frame of (WM)^2 - World Meeting for Women in Mathematics-2022.

This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent survey papers in the area.