Some properties of tensor centre of groups
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Let G⊗G be the tensor square of a group G. The set of all elements a in G such that a⊗g = 1_⊗, for all g in G, is called the tensor centre of G and denoted by Z^⊗(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 k : G ⊗ G → G'.
Abstract
Let G⊗G be the tensor square of a group G. The set of all elements a in G such that a⊗g = 1_⊗, for all g in G, is called the tensor centre of G and denoted by Z^⊗(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 k : G ⊗ G → G'.
참고문헌 (9)
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