M. R. R. Moghaddam , P. Niroomand , S. H. Jafari
J. Korean Math. Soc - 46, 2, 249—256. -February, 2009 - .
Publication year: 2009

Let $\small{G{\otimes}G}$ be the tensor square of a group G. The set of all elements a in G such that $\small{a{\otimes}g\;=\;1_{\otimes}}$, for all g in G, is called the tensor centre of G and denoted by $\small{Z^{\otimes}^}$(G). In this paper some properties of the tensor centre of G are obtained and the capability of the pair of groups (G, G’) is determined. Finally, the structure of $\small{J_2}$(G) will be described, where $\small{J_2}$(G) is the kernel of the map $\small{\kappa}$ : $\small{G{\otimes}\;{\rightarrow}\;G$.