Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SOME PROPERTIES OF TENSOR CENTRE OF GROUPS

  • Moghaddam, Mohammad Reza R. (FACULTY OF MATHEMATICAL SCIENCES FERDOWSI UNIVERSITY OF MASHHAD, KHAYYAM HIGHER EDUCATION INSTITUTE) ;
  • Niroomand, Payman (PAYMAN NIROOMAND FACULTY OF MATHEMATICAL SCIENCES FERDOWSI UNIVERSITY OF MASHHAD) ;
  • Jafari, S. Hadi (FACULTY OF MATHEMATICAL SCIENCES FERDOWSI UNIVERSITY OF MASHHAD)
  • Published : 2009.03.31
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Abstract

Let $G{\otimes}G$ be the tensor square of a group G. The set of all elements a in G such that $a{\otimes}g\;=\;1_{\otimes}$, for all g in G, is called the tensor centre of G and denoted by $Z^{\otimes}^$(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 $J_2$(G) will be described, where $J_2$(G) is the kernel of the map $\kappa$ : $G{\otimes}\;{\rightarrow}\;G'$.

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References

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