“presentation”的概念、定义、翻译、参考文献-科学参考

presentation

Mathematics

A description of a group in terms of generators and relations. For example, 〈x | xⁿ = e〉 is a group with a single generator x of order n and so is the cyclic group of order n. The dihedral group D_2n has the presentation

$〈 r, s | r^{n} = e = s^{2}, s r = r^{- 1} s 〉 .$

Words in the generators are equal if and only the relations can be used to show this. Formally, the presentation defines a group as the quotient group of the free group on the set of generators by the normal subgroup generated by the relations.

单词	presentation
释义	presentation Mathematics A description of a group in terms of generators and relations. For example, 〈x \| xⁿ = e〉 is a group with a single generator x of order n and so is the cyclic group of order n. The dihedral group D_2n has the presentation $〈 r, s \| r^{n} = e = s^{2}, s r = r^{- 1} s 〉 .$ Words in the generators are equal if and only the relations can be used to show this. Formally, the presentation defines a group as the quotient group of the free group on the set of generators by the normal subgroup generated by the relations.
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