A new characterization of groups $\mathbf{ B_4 (q )}$

Abstract

One of an important problems in finite groups theory is, characterizable of groups by specific property. In this paper, we prove that groups $B_4 (q)$, where $3< q$ be prime number and $ \frac{q^4+1}{2}$ is a prime number, can be uniquely determined by the largest elements order and the order of group.