On the influence of the indices of normalizers of Sylow subgroups on the structure of a finite -soluble group.
On the intersection of maximal non-supersoluble subgroups in a finite group
Gli autori studiano il sottogruppo intersezione dei sottogruppi massimali e non supersolubili di un gruppo finito e le relazioni tra la struttura di e quella di .
On the Isomorphism of Group Algebras.
On the isomorphism problem for modular group algebras of elementary abelian-by-cyclic p-groups
Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.
On the largest conjugacy class size in a finite group
On the lattice automorphisms of and
On the lattice of pronormal subgroups of dicyclic, alternating and symmetric groups
In this paper, the structures of collection of pronormal subgroups of dicyclic, symmetric and alternating groups are studied in respect of formation of lattices and sublattices of . It is proved that the collections of all pronormal subgroups of and S do not form sublattices of respective and , whereas the collection of all pronormal subgroups of a dicyclic group is a sublattice of . Furthermore, it is shown that and ) are lower semimodular lattices.
On the Loewy-series of the modular group algebra of a finite p-group.
On the maximal subgroups of the finite classical groups.
On the monomiality of groups whose third derived group is trivial.
On the noncommuting graph associated with a finite group.
On the (non-)contractibility of the order complex of the coset poset of an alternating group
On the normalizer of a group in the Cayley representation.
On the number of conjugacy classes in a finite group
On the number of conjugacy classes of pi-elements in a finite group
On the number of generating pairs for the groups and .
On the number of maximal theta pairs in a finite group
On the number of normal subgroups of a given prime index
On the number of solutions of equation in a finite group
Theorem A yields the condition under which the number of solutions of equation in a finite -group is divisible by (here is a fixed positive integer). Theorem B which is due to Avinoam Mann generalizes the counting part of the Sylow Theorem. We show in Theorems C and D that congruences for the number of cyclic subgroups of order which are true for abelian groups hold for more general finite groups (for example for groups with abelian Sylow -subgroups).
On the Occurrence of the Complete Graph in the Hasse Graph of a Finite Group