A new characterization of Mathieu-groups by the order and one irreducible character degree

A Characterization of the Suzuki Groups by Order and the Largest Elements Order

One of the important problems in group theory is characterization of a group by a given property, that is, to prove there exist only one group with a given property. Let  be a finite group. We denote by  the largest order of elements of . In this paper, we prove that some Suzuki groups are characterizable by order and the largest order of elements. In fact, we prove that if  is a group with  an...

A Characterization of the Small Suzuki Groups by the Number of the Same Element Order

Suppose that  is a finite group. Then the set of all prime divisors of  is denoted by  and the set of element orders of  is denoted by . Suppose that . Then the number of elements of order  in  is denoted by  and the sizes of the set of elements with the same order is denoted by ; that is, . In this paper, we prove that if  is a group such that , where , then . Here  denotes the family of Suzuk...

characterization of some simple $k_4$-groups by some irreducible complex character degrees

in this paper, we examine that some simple $k_4$-groups can be determined uniquely by their orders and one or two irreducible complex character degrees.

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