Some results on β-degree respect to the Burnside variety

In 2009, Tarnauceanu introduced the concept of subgroup commutativity degree of finite group G. Th is concept is arising interest in several areas of group theory. In this paper, at first, we define β-degree respect to the Burnside variety. dβ(G) is the β-degree of a group G. We show that if G and H are two isologism groups, then dβ(G) = dβ(H). Finally, we generalize this concept to subgroup Burnside degree and give some results on this.