Generating random elements in finite groups.
Generation of finite groups by nilpotent subgroups
We study the generation of finite groups by nilpotent subgroups and in particular we investigate the structure of groups which cannot be generated by nilpotent subgroups and such that every proper quotient can be generated by nilpotent subgroups. We obtain some results about the structure of these groups and a lower bound for their orders.
Generators for finite groups with a unique minimal normal subgroup
Generic Fixed Point Free Action of Arbitrary Finite Groups.
Groupes dont le centralisateur d'un sous-groupe est d'ordre borné.
Groups as the union of proper subgroups.
Groups in which the prime graph is a tree
The prime graph of a finite group is defined as follows: the set of vertices is , the set of primes dividing the order of , and two vertices , are joined by an edge (we write ) if and only if there exists an element in of order . We study the groups such that the prime graph is a tree, proving that, in this case, .
Groups of Prime-Power Order Having an Abelian Centralizer of Type (r, 1).
Groups with the same orders of Sylow normalizers as the Mathieu groups.
Groups with the same prime graph as an almost sporadic simple group.
Growth in
Gruppi finiti risolubili in cui tutti i sottogruppi subnormali hanno difetto al più