On the Fitting length of
On the functorial method for studying the lattices of subgroups of finite groups.
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 largest conjugacy class size in a finite group
On the monomiality of groups whose third derived group is trivial.
On the -length of the product of two Shmidt groups.
On the -supersolubility of a finite group with a -supplemented Sylow -subgroup.
On the prefrattini subgroups of finite soluble groups.
On the product of two n-decomposable soluble groups.
On the Shemetkov problem for Fitting classes.
On the solvability of commutative loops and their multiplication groups
We investigate the situation when the inner mapping group of a commutative loop is of order , where is a prime number, and we show that then the loop is solvable.
On the structure of finite loop capable Abelian groups
Loop capable groups are groups which are isomorphic to inner mapping groups of loops. In this paper we show that abelian groups , where and is an odd prime, are not loop capable groups. We also discuss generalizations of this result.
On the structure of finite loop capable nilpotent groups
In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either , as the Sylow -subgroup for some odd prime or the group of quaternions as the Sylow -subgroup may not be loop capable.
On the structure of solvable -groups
On the Theory of Fitting Classes of Finite Soluble Groups.
On TI-subgroups and QTI-subgroups of finite groups
Let be a group. A subgroup of is called a TI-subgroup if or for every and is called a QTI-subgroup if for any . In this paper, a finite group in which every nonabelian maximal is a TI-subgroup (QTI-subgroup) is characterized.
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...
On weakly-supplemented subgroups and the solvability of finite groups
A subgroup of a finite group is weakly-supplemented in if there exists a proper subgroup of such that . In this paper, some interesting results with weakly-supplemented minimal subgroups or Sylow subgroups of are obtained.
On weakly-supplemented subgroups of finite groups
A subgroup of a finite group is weakly-supplemented in if there exists a proper subgroup of such that . In this paper, some interesting results with weakly-supplemented minimal subgroups to a smaller subgroup of are obtained.