On a class of commutative groupoids determined by their associativity triples
Let be a commutative groupoid such that ; ; or . Then is determined uniquely up to isomorphism and if it is finite, then for an integer .
On a class of distributive Steiner quasigroups
On a class of finite solvable groups
A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group...
On a class of groupoids
On a class of groups with Lagrangian factor groups.
On a class of groups with strongly embedded subgroup.
On a Class of Jordan Groups.
On a class of locally Butler groups
A torsionfree abelian group is called a Butler group if for any torsion group . It has been shown in [DHR] that under any countable pure subgroup of a Butler group of cardinality not exceeding is again Butler. The purpose of this note is to show that this property has any Butler group which can be expressed as a smooth union of pure subgroups having countable typesets.
On a class of locally completely decomposable Abelian groups
On a class of modular numerical semigroups.
On a class of Moufang loops
On a Class of N-ary Quasigroups
On a class of n-ary quasigroups.
On a class of residually finite groups.
On a class of semigroups admitting ring structure.
On a class of semigroups with symmetric presentations.
On a class of semisimple semigroups.
On a class of subdirectly irreducible groupoids
On a class of t-archimedean semigroups.
On a class of torsionfree Abelian groups [Abstract of thesis]