O jistých grupách matic
On - and -decomposable finite groups
On - and -decomposable finite groups
On a class of groups with strongly embedded subgroup.
On a question of Deaconescu about automorphisms
On a question of Deaconescu about automorphisms. - II
On deficient products in infinite groups
On groups with many nearly maximal subgroups
A subgroup of a group is nearly maximal if the index is infinite but every subgroup of properly containing has finite index, and the group is called nearly if all its subgroups of infinite index are intersections of nearly maximal subgroups. It is proved that an infinite (generalized) soluble group is nearly if and only if it is either cyclic or dihedral.
On minimal non-PC-groups
A group is said to be a PC-group, if is a polycyclic-by-finite group for all . A minimal non-PC-group is a group which is not a PC-group but all of whose proper subgroups are PC-groups. Our main result is that a minimal non-PC-group having a non-trivial finite factor group is a finite cyclic extension of a divisible abelian group of finite rank.
On non-periodic groups whose finitely generated subgroups are either permutable or pronormal
The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group is called a generalized radical, if has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the followingTheorem. Let be a locally generalized radical...
On some groups with almost regular element of prime order.
On subsemigroup lattices of aperiodic groups.
On the exponent of the product of two groups
On the group of reduced identities of relatively free solvable groups.
On the Structure of the Normal Subgroups of a Group: Nilpotency.