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

The equilibrium real exchange rate of China: a productivity approach

A large body of theoretical and empirical works asserts that exchange rates depend upon a country's productivity growth, and this effect is dubbed the Balassa-Samuelson effect. This paper examines the evidence for a Balassa-Samuelson based explanation for the real exchange rate movements of China vis-a-vis the U.S. dollar. Using disaggregated industry level data, we construct sectoral total factor productivities (TFPs) for the tradable and nontradable sectors from 1980-2003. Our main findings are: (a) the sectoral TFP differential is cointegrated with the relative price of nontradables with the unit cointegration vector; and (b) the real exchange rate is cointegrated with home and foreign sectoral TFP differentials. This productivity based real exchange rate model is then used to estimate the equilibrium exchange rates of the Renminbi (RMB). A comparison of the equilibrium exchange rate predicted by the productivity-based model and the actual rate indicates that the Renminbi is somewhat undervalued against the US dollar, though the undervaluation is not statistically significant. Our conclusions continue to hold even after we have controlled for the movements of net foreign assets.Nontraded Goods; Balassa-Samuelson Model; Cointegration