Conjugately biprimitively finite groups with the primary minimal condition (Q1060290)

The author continues the study of conjugately biprimitively finite groups which were introduced by Shunkov. By definition a group G is conjugately biprimitively finite if for any finite subgroup H of G each pair of elements of equal prime order from \(N_ G(H)/H\) generates a finite subgroup of \(N_ G(H)/H\). It is proved that if a group satisfying the condition of the title is periodic then it is locally finite. It is also proved that if a group satisfying the condition of the title has only finite Sylow p-subgroups then it has a unique maximal periodic subgroup.