Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

We describe a practical algorithm for computing representatives of the conjugacy classes of maximal subgroups in a finite group, together with details of its implementation for permutation groups in the MAGMA system. We also describe methods for computing complements of normal subgroups and minimal supplements of normal soluble subgroups of finite groups.

THEOREM 2. If G is a finite monolithic group with monolith M (in other words, if G is a finite group with a unique minimal normal subgroup M), then Mis a verbal subgroup ofG. These generalize the corresponding results for finite ^-groups established by Weichsel ((4), Theorems 2-1, 2-3). The second answers affirmatively a (privately communicated) question of Sheila Oates. In order to give our de...

In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.

Abstract A group G is said to be an FC -group if every conjugacy class of has finite order and a T subnormal subgroup normal in . In this paper we give characterization groups that are both -groups go further the study with few non-normal subgroups sense chain conditions. The structure satisfying maximal, minimal double condition on will described.