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Ifa is an age long divination system vastly consulted across west Africa, the Caribbeans and the Americas. The system goes with the use of signature codes named Odu Ifa which are 256 in number consisting of 16 Oju Odu (major) and 240 Omo Odu (minor). We consider the algebraic structure of this divination system by writing the codes representing the main Odu as 4 × 2 matrices which are found to satisfy group axioms under addition mod 2. We construct the Cayley table that gives an abelian group which we dubbed “self-inversed group”. Other properties of group structure are outlined.

We study several weak Engel conditions on linear groups, starting from the “almost Engel” condition of Khukhro and Shumyatsky. There the groups were Engel modulo certain finite subsets. Here we replace “finite subsets” by “Chernikov subgroups” in one case and “polycyclic-by-finite subgroups” in another. We also include a shorter proof of a theorem of Shumyatsky characterizing linear almost Engel groups.

Determining the affine equivalence of Boolean functions has significant applications in circuit and cryptography. Previous methods for determining this require a large amount of computation when Boolean functions are bent functions or when the truth table is sparse. This paper presents a new method to determine the affine equivalence based on matrix algebra. By transforming Boolean function to the corresponding matrix representation, we first propose and prove the congruent standard form of Boolean function. It lays the foundation for the determination of equivalence because affine Boolean functions must have the same standard form. Then we find the generators of orthogonal matrix group and symplectic matrix group, which greatly reduce the search space. The computation complexity of our method is o(2(r2/2+n*(n-r))), where n is the number of bit operations, and r is the rank of the matrix, which is the product of Boolean-1 matrix of the test Boolean function and its transposition. The experimental results show that our method is useful when the test Boolean function is no more than 7 bits and r is greater than 2.