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 (non-)contractibility of the order complex of the coset poset of an alternating group
On the Occurrence of the Complete Graph in the Hasse Graph of a Finite Group
On the prefrattini subgroups of finite soluble groups.
On the total number of principal series of a finite abelian group.
On uniform dimensions of finite groups
Let G be any finite group and L(G) the lattice of all subgroups of G. If L(G) is strongly balanced (globally permutable) then we observe that the uniform dimension and the strong uniform dimension of L(G) are well defined, and we show how to calculate these dimensions.