Finite Groups with Certain Permutability Criteria

Finite groups in which normality, permutability or Sylow permutability is transitive

Y. Li gave a characterization of the class of finite soluble groups in which every subnormal subgroup is normal by means of NE -subgroups: a subgroup H of a group G is called an NE -subgroup of G if NG(H) ∩ H = H. We obtain a new characterization of these groups related to the local Wielandt subgroup. We also give characterizations of the classes of finite soluble groups in which every subnorma...

On a graph related to permutability in finite groups

For a finite group G we define the graph Γ(G) to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes A, B are joined by an edge if for some A ∈ A, B ∈ B A and B permute. We characterise those groups G for which

On the subgroup permutability degree of some finite simple groups

Consider a finite group G and subgroups H,K of G. We say that H and K permute if HK = KH and call H a permutable subgroup if H permutes with every subgroup of G. A group G is called quasi-Dedekind if all subgroups of G are permutable. We can define, for every finite group G, an arithmetic quantity that measures the probability that two subgroups (chosen uniformly at random with replacement) per...

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