On finite groups of whose all proper subgroups are


Hossein AndikfarAli Reza Ashrafi


Abstract

carpathian_2006_22_001_005_abstract

Full PDF

carpathian_2006_22_001_005

A finite group G is called w-cyclic, if G has at most d subgroup, for all divisors d of |G|. In this paper, we study the structure of a finite group all of whose proper subgroups are w-cyclic. In the case that G has prime power order, we prove that such a group is elementary abelian of order p2, p is prime, the quaternion group Q8 or the generalized quaternion group Q16. We prove that if such a G is not a p-group, then G is solvable and in some cases, we obtain the structure of G. Finally, we characterize the finite groups with w-cyclic proper quotient groups.

Additional Information

Author(s)

Andikfar, Hossein, Ashrafi, Ali Reza