This paper investigates a novel characterization method for the sporadic simple group B (Baby Monster Group). Using the combination of the order component set OC (G) of a finite group and the set 䂷 (G) of the orders of centralizers of elements of highest order within the group, we proved: a finite group G is isomorphic to the sporadic simple group B if and only if the following two conditions hold: (1) G shares the same largest order component m₁ (G) as B; (2) The sets 䂷 (G) and 䂷 (B) of the orders of centralizers of their respective highest-order elements are identical. By analyzing the prime graph structure, excluding the possibility of Frobenius groups and 2-Frobenius groups, and utilizing the Classification Theorem of Finite Simple Groups, we ultimately establish the sufficiency and necessity of these characterizing conditions.
Lan et al. (Wed,) studied this question.