On a question of Chambers and Makan.
On supplements of subgroups of finite groups
In this paper the concept of s-pair for a subgroup of a finite group is introduced and studied. It provides a uniform way to study the influence of some families of subgroups on the structure of a finite group. A criterion for a finite group to belong to a saturated formation and necessary and sufficient conditions for solubility, supersolvability and nilpotence of a finite group are given.
On minimal non-supersoluble groups.
-normally embedded subgroups of finite soluble groups
Infinite groups with many permutable subgroups.
On -normally embedded subgroups of finite soluble groups
On some permutable products of supersoluble groups.
It is well known that a group G = AB which is the product of two supersoluble subgroups A and B is not supersoluble in general. Under suitable permutability conditions on A and B, we show that for any minimal normal subgroup N both AN and BN are supersoluble. We then exploit this to establish some sufficient conditions for G to be supersoluble.
Local classes and pairwise mutually permutable products of finite groups.
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