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
Hajós' theorem and the partition lemma.
Hall pi-subgroups and conjugacy classes
Homomorphisms of triangle groups with large injectivity radius.
Huppert’s conjecture for
Intersection graphs of subgroups of finite groups
In this paper we classify finite groups with disconnected intersection graphs of subgroups. This solves a problem posed by Csákány and Pollák.
Inverse zero-sum problems in finite Abelian p-groups
We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible length over...
Irreducible characters of a Sylow p-subgroup of the orthogonal group.
Landau's theorem for p-blocks of p-solvable groups.
Maximal subgroups of finite groups.
Maximal sum-free sets and block designs
Minimal abelian automorphism groups of finite groups
Minimality of an active fragment of the character table of a finite group.
Modular representations and almost free actions.