On equationally compact semigroups.
We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order are centrally nilpotent of class at most two.
We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order are centrally nilpotent of class at most two.
Let be a finite commutative loop and let the inner mapping group , where is an odd prime number and . We show that is centrally nilpotent of class two.
In this paper we consider finite loops and discuss the following problem: Which groups are (are not) isomorphic to inner mapping groups of loops? We recall some known results on this problem and as a new result we show that direct products of dihedral 2-groups and nontrivial cyclic groups of odd order are not isomorphic to inner mapping groups of finite loops.
We investigate the situation that the inner mapping group of a loop is of order which is a product of two small prime numbers and we show that then the loop is soluble.
In this paper we study some interesting properties of regular ternary semigroups, completely regular ternary semigroups, intra-regular ternary semigroups and characterize them by using various ideals of ternary semigroups.