An Example of a Right Loop Admitting Only Discrete Topolization

Being motivated by \cite{sk} and \cite{nms}, an example of a right loop admitting only discrete topolization is given

Solvable and Nilpotent Right Loops

In this paper the notion of nilpotent right transversal and solvable right transversal has been defined. Further, it is proved that if a core-free subgroup has a generating solvable transversal or a generating nilpotent transversal, then the whole group is solvable.Comment: arXiv admin note: substantial text overlap with arXiv:1307.539

Some Characterizations of a Normal Subgroup of a Group

Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this note, we give some characterizations for normality of H in G. As a consequence we get a very short and elementary proof of the Main Theorem of [5], which avoids the use of the classification of finite simple group