On the computational complexity of the theory of Abelian groups
Using the Ehrenfeucht games method, the decidability and complexity of the following first-order theories is obtained: the theory of the divisible and indecomposable p-groups, the theory of the groups of rational numbers with denominators prime to p, the theory of cyclic groups of prime power order, the theory of direct sums of countably many infinite cyclic groups, the theory of finite Abelian groups, the theory of all Abelian groups. The author has also confirmed Gurevich's conjecture stating that the theory of all Abelian groups is elementary.
groups of rational numbers with denominators prime to p
direct sums of countably many infinite cyclic groups
scientific article; zbMATH DE number 4041862