Products of conjugacy classes in simple groups

Co-authored with J. Moori. To appear in QM.

In this paper, we study a conjecture due to
Arad and Herzog which asserts that in a finite non-abelian simple group the
product of two nontrivial conjugacy classes is never a single conjugacy class.
In particular, we will verify this conjecture for several families of finite simple
groups of Lie type

The Simple Ree groups are determined by the set of their character degrees

to appear in J. Algebra

In this paper, we verify Huppert's Conjecture for the simple Ree groups.

Rank 3 permutation characters and maximal subgroups

This paper is part of my PhD thesis.

Influence of strongly closed 2-subgroups on the structure of finite groups

published in Glasgow Mathematical Journal

In this paper, we
investigate the structure of a group G under the assumption that
every subgroup of order 2^m (and 4 if m=1) of a  2-Sylow
subgroup S of G is strongly closed in S with respect to G.

Symmetric groups are determined by their character degrees

published in Journal of Algebra

We proved that the symmetric groups are uniquely determined by the structure of their complex group algebras.

On Huppert's Conjecture for the Monster and Baby Monster

Co-author with T.P. Wakefield, published in Monatshefte für Mathematik

We verify Huppert's Conjecture for the Monster and Baby Monster Sporadic simple groups.

Simple exceptional groups of Lie type are determined by their character degrees

published in Monatshefte für Mathematik

This is the second paper in the series of papers to verify the conjecture which says that the nonabelian simple groups are uniquely determined by the first columns of their ordinary character tables or equivalently by the structure of their complex group algebras.

Alternating and Sporadic simple groups are determined by their character degrees

published in Algebras and Representation Theory

We showed that the simple groups in the title are uniquely determined by their character degrees (counting multiplicities) and so they are determined by the first columns of their ordinary character tables

Groups with normal restriction property

published in 'Arch. Math', 2009

Let G be a finite group. A subgroup M of G is said to be an NR-subgroup if, whenever K is normal in M, then K^ G ∩ M = K where K^ G is the normal closure of K in G. Using the Classification of Finite Simple Groups, we prove that if every maximal subgroup of G is an NR-subgroup then G is solvable. This gives a positive answer to a conjecture posed in Berkovich (Houston J. Math. 24 (1998), 631–638)

Rank 3 Permutation Characters and Maximal Subgroups-PhD Thesis

Ph.D Thesis

The character containments of permutation characters of nearly simple primitive rank 3 groups acting on non-singular points are classified and its application to the study of minimal genus of algebraic curves which admit group actions is given.

Normal restriction in finite groups

published in "Communications in Algebra", 2011

We proved some sufficient conditions for the solvability of finite groups which possess many NR-subgroups. We also proved a criterion for the existence of a normal p-complement in finite groups.

Character degree sums in finite nonsolvable groups

"Co-authored with K. Magaard". Published in J. Group Theory.

Let N be a minimal normal nonabelian subgroup of a finite group G. We will show that there exists a nontrivial irreducible character of N of degree at least 5 which is extendible to G. This result will be used to settle two open questions raised by Berkovich and Mann, and Berkovich and Zhmud.