Element orders and Sylow structure of finite groups

Classification of finite simple groups whose Sylow 3-subgroups are of order 9

In this paper, without using the classification of finite simple groups, we determine the structure of  finite simple groups whose Sylow 3-subgroups are of the order 9. More precisely, we classify finite simple groups whose Sylow 3-subgroups are elementary abelian of order 9.

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...

Invariant Sylow subgroups and solvability of finite groups

Let A and G be finite groups of relatively prime orders and assume that A acts on G via automorphisms. We study how certain conditions on G imply its solvability when we assume the existence of a unique A-invariant Sylow p-subgroup for p equal to 2 or 3. Mathematics Subject Classification (2010). Primary 20D20; Secondary 20D45.

A new characterization of $L_2(q)$ by the largest element orders

‎We characterize the finite simple groups $L_2(q)$ by the group orders and the largest‎ ‎element orders‎, ‎where $q$ is a prime or $q=2^a$‎, ‎with $2^a+1$ or $2^a-1$ a prime‎.  

Finite Groups with p-Sylow Coverings