On cover-avoiding subgroups of Sylow subgroups of finite groups
On disjoint covering of groups by their cosets
On finite minimal non-p-supersoluble groups
If ℱ is a class of groups, then a minimal non-ℱ-group (a dual minimal non-ℱ-group resp.) is a group which is not in ℱ but any of its proper subgroups (factor groups resp.) is in ℱ. In many problems of classification of groups it is sometimes useful to know structure properties of classes of minimal non-ℱ-groups and dual minimal non-ℱ-groups. In fact, the literature on group theory contains many results directed to classify some of the most remarkable among the aforesaid classes. In particular, V....
On fully unsaturated homomorphs of finite groups
On groups for which the lattice of normal subgroups is distributive
On groups of odd order admitting an elementary 2-group of automorphisms
On imprimitive groups with small degree
On index preserving projectivities of finite groups
On infinite partition representations and their finite quotients
On lattice automorphisms of the special linear group
We show, with a counterexample, that proposition 3 in [2], as it stands, is not correct; we prove however that by changing the hypothesis the thesis of the proposition remains still valid.
On lattice properties of S-permutably embedded subgroups of finite soluble groups
In this paper we prove the following results. Let π be a set of prime numbers and G a finite π-soluble group. Consider U, V ≤ G and such that and . Suppose also is a Hall π-sub-group of some S-permutable subgroup of G. Then and . Therefore,the set of all S-permutably embedded subgroups of a soluble group G into which a given Hall system Σ reduces is a sublattice of the lattice of all Σ-permutable subgroups of G. Moreover any two subgroups of this sublattice of coprimeorders permute.
On n-Sum Groups.
On -groups whose -automorphism group is transitive on the atoms
On Partial Ordering of Chief Factors in Solvable Groups.
On the dimension of finite permutation group actions.
On the Dirichlet polynomial of finite group of Lie type
On the Fitting length of
On the functorial method for studying the lattices of subgroups of finite groups.
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.