“direct product”的概念、定义、翻译、参考文献-科学参考

direct product

Mathematics

Computer

of two groups G and H with group operations ρ‎ and τ‎ respectively. The group consisting of the elements in the Cartesian product of G and H and on which there is a dyadic operation ∘ defined as follows:
$(g_{1}, h_{1}) \circ (g_{2}, h_{2}) = (g_{1} ρ g_{2}, h_{1} τ h_{2})$
The identity of this group is then just (e_G,e_H), where e_G and e_H are the identities of groups G and H respectively. The inverse of (g,h) is then (g⁻¹,h⁻¹).
These concepts can be generalized to deal with the direct product of any finite number of groups on which there are specified group operations.

单词	direct product
释义	direct product Mathematics See product group, semi-direct product. Computer of two groups G and H with group operations ρ‎ and τ‎ respectively. The group consisting of the elements in the Cartesian product of G and H and on which there is a dyadic operation ∘ defined as follows: $(g_{1}, h_{1}) \circ (g_{2}, h_{2}) = (g_{1} ρ g_{2}, h_{1} τ h_{2})$ The identity of this group is then just (e_G,e_H), where e_G and e_H are the identities of groups G and H respectively. The inverse of (g,h) is then (g⁻¹,h⁻¹). These concepts can be generalized to deal with the direct product of any finite number of groups on which there are specified group operations.
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