FINITE SOLVABLE GROUPS HAVING A UNIQUE IRREDUCIBLE CHARACTER OF A GIVEN DEGREE

Finite Groups with a Unique Nonlinear Nonfaithful Irreducible Character

In this paper, we consider finite groups with precisely one nonlinear nonfaithful irreducible character. We show that the groups of order 16 with nilpotency class 3 are the only p-groups with this property. Moreover we completely characterize the nilpotent groups with this property. Also we show that if G is a group with a nontrivial center which possesses precisely one nonlinear nonfaithful ir...

Classification of solvable groups with a given property

In this paper we classify all finite solvable groups satisfying the following property P5: their orders of representatives are set-wise relatively prime for any 5 distinct non-central conjugacy classes.

Finite p-groups with few non-linear irreducible character kernels

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

On Finite Groups With Two Irreducible Character Degrees

The Tensor Degree of a Pair of Finite Groups

In this paper, we study the tensor commutativity degree of pair of finite groups. Erdos introduced the relative commutativity degree and studied its properties. Then, Mr. Niroomand introduced the tensor relative commutativity degree, calculated tensor relative degree for some groups, and studied its properties. Also, he explained its relation with relative commutativity degree. In this paper, w...