Finite soluble groups with certain splitting properties

certain finite abelian groups with the redei k-property

‎three infinite families of finite abelian groups will be‎ ‎described such that each member of these families has‎ ‎the r'edei $k$-property for many non-trivial values of $k$‎.

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

certain finite abelian groups with the redei $k$-property

‎three infinite families of finite abelian groups will be‎ ‎described such that each member of these families has‎ ‎the r'edei $k$-property for many non-trivial values of $k$‎.

Finite subnormal coverings of certain solvable groups

A group is said to have a finite covering by subgroups if it is the set theoretic union of finitely many subgroups. A theorem of B. H. Neumann [11] characterizes groups with finite coverings by proper subgroups as precisely those groups with finite non-cyclic homomorphic images. R. Baer (see [13, Theorem 4.16]) proved that a group has a finite covering by abelian subgroups if and only if it is ...

Finite Groups With a Certain Number of Cyclic Subgroups

In this short note we describe the finite groups G having |G| − 1 cyclic subgroups. This leads to a nice characterization of the symmetric group S3. In subgroup lattice theory, it is a usual technique to associate to a finite group G some posets of subgroups of G (see, e.g., [4]). One such poset is the poset of cyclic subgroups of G, usually denoted by C(G). Notice that there are few papers on ...