Groupes finis

In the paper new criteria of existence and conjugacy of Hall subgroups of finite groups are given.

This paper extends the study of group algebras of finite groups in which the socle of the center is an ideal. We provide a detailed analysis of the structure of these groups. In a particular case, we reach a complete characterization of the groups with this property.

This is the text of my Bourbaki seminar on the proof of the surface subgroup conjecture by Jeremy Kahn and Vladimir Markovic.

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

- Synth\`ese des travaux pr\'esent\'es en vue d'une Habilitation \`a Diriger des Recherches - Synthesis of works presented towards the Habilitation degree This is a summary (in French) of my work in number theory, group theory and combinatorics in the last eight years.

This is the third and final installment of an exposition of an ACL2 formalization of finite group theory. Part I covers groups and subgroups, cosets, normal subgroups, and quotient groups. Part II extends the theory in the developmnent of group homomorphisms and direct products, which are applied in a proof of the Fundamental Theorem of Finite Abelian Groups. The central topics of the present paper are the symmetric groups and the Sylow theorems, which pertain to subgroups of...

This paper surveys basic properties of finite presentation in groups, Lie algebras and rings. It includes some new results and also new, more elementary proofs, of some results that are already in the literature. In particular, we discuss examples of Stallings and of Roos on coherence by using a purely algebraic, nonhomological, approach.

One of the classical problems in group theory is determining the set of positive integers $n$ such that every group of order $n$ has a particular property $P$, such as cyclic or abelian. We first present the Sylow theorems and the idea of solvable groups, both of which will be invaluable in our analysis. We then gather various solutions to this problem for cyclic, abelian, nilpotent, and supersolvable groups, as well as groups with ordered Sylow towers. This work is an expo...

This is a collection of questions that I am considering submitting to the next edition of the Kourovka Notebook of open questions in group theory. Most are questions I raised in papers between 1981 and the present; a few are new. I welcome feedback.

We present an accessible introduction to basic results on groups of intermediate growth.