On Solvable Groups with a Minimal Normal P-Subgroup
On some maximal -quasinormal subgroups of finite groups.
On some permutable products of supersoluble groups.
It is well known that a group G = AB which is the product of two supersoluble subgroups A and B is not supersoluble in general. Under suitable permutability conditions on A and B, we show that for any minimal normal subgroup N both AN and BN are supersoluble. We then exploit this to establish some sufficient conditions for G to be supersoluble.
On S-quasinormal subgroups of finite 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 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 maximal subgroups of the finite classical groups.
On the -length of the product of two Shmidt groups.
On the -supersolubility of a finite group with a -supplemented Sylow -subgroup.
On the product of two n-decomposable soluble groups.
On the rarity of quasinormal subgroups
On the total number of principal series of a finite abelian group.
On weakly -permutably embedded subgroups
Suppose is a finite group and is a subgroup of . is said to be -permutably embedded in if for each prime dividing , a Sylow -subgroup of is also a Sylow -subgroup of some -permutable subgroup of ; is called weakly -permutably embedded in if there are a subnormal subgroup of and an -permutably embedded subgroup of contained in such that and . We investigate the influence of weakly -permutably embedded subgroups on the -nilpotency and -supersolvability of finite...
Periodic linear groups factorized by mutually permutable subgroups
The aim is to investigate the behaviour of (homomorphic images of) periodic linear groups which are factorized by mutually permutable subgroups. Mutually permutable subgroups have been extensively investigated in the finite case by several authors, among which, for our purposes, we only cite J. C. Beidleman and H. Heineken (2005). In a previous paper of ours (see M. Ferrara, M. Trombetti (2022)) we have been able to generalize the first main result of J. C. Beidleman, H. Heineken (2005) to periodic...
Prodotti di sottogruppi mutuamente permutabili
Products of finite nilpotent groups.
Products of trees, lattices and simple groups.
Produkte endlicher einfacher Gruppen.
Pronormal and subnormal subgroups and permutability
We describe the finite groups satisfying one of the following conditions: all maximal subgroups permute with all subnormal subgroups, (2) all maximal subgroups and all Sylow -subgroups for permute with all subnormal subgroups.
Schreier type theorems for bicrossed products
We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups (H;G; α; β) is deformed using a combinatorial datum (σ; v; r) consisting of an automorphism σ of H, a permutation v of the set G and a transition map r: G → H in order to obtain a new matched pair (H; (G; *); α′, β′) such that there exists a σ-invariant isomorphism of groups H α⋈β G ≅H α′⋈β′ (G, *). Moreover, if we fix the group H and the automorphism σ ∈ Aut H then...