《Galois theory》 H.E. p. 56 (S42) * * * 15:23 Fifth Exercise Set 1. Show that a set of substitutions of n objects a, b, c, ... is a group if and only if it is closed under composition. ---- 置换的集合构成群当且仅当它在复合运算之下封闭。 . 证明：1) 置换的集合(记作 ...
《Galois theory》 H.E. p. 55 (S42) * * * 18:33 第四段 As a final example, consider the equation x^4 + 1 = 0 (the equation for the primitive 8th roots of unity). ---- 作为最后的例子，考虑方程x^4 + 1 = 0(本原8次单位根的方程)。 . 评论：此例是 x^p - k = 0 的特 ...
《Galois theory》 H.E. p. 55 (S42) * * * ？？？ 第三段 Another example of interest is an equation of the form x^p = k where the known quantities K include k and a primitive pth root of unity α (with p prime). ---- 另一个有用的例子是形如 x^p = k 的方程，其中已知量 K 包 ...
《Galois theory》 H.E. p. 54~55 (S42) * * * 9:14 第二段 His other example is the group of the equation x^(p-1) + x^(p-2) + ... + x + 1 = 0 satisfied by the primitive pth roots of unity where p is prime. ---- 他的另一个例子是方程x^(p-1) + x^(p-2) + ... + x + 1 = 0， ...
《Galois theory》 H.E. p. 54 (S42) * * * 10:44 第一段 Galois gives two examples of Galois groups of equations. ---- 伽罗瓦给出了方程的伽罗瓦群的两个例子。 . The first is what he calls an “algebraic” equation, by which he means an equation in which the coefficients ...
《Galois theory》 H.E. p. 57 (S43) * * * ??? 第三段 If the expression of a root involves taking a j th root and j is not prime, then j = j 1 j 2 where j 1 and j 2 are smaller ...
注：下文是群邮件的内容。 《Galois theory》 H.E. p. 58 (S43) * * * 11: 51 第五段 Thus, if the given equation f(x) = 0 is solvable by radicals, there is a sequence of fields K⊂K'⊂K''⊂ ... ⊂K^(μ),... - ...
《Galois theory》 H.E. p. 58 (S43) * * * 11: 13 第七段 The main step in Galois' analysis of solvable equations is to... ---- 伽罗瓦对于可解方程的分析的主要步骤是... . ... study the way the group of an equation can be reduced by the adjunction of a pth root ...
注：下文是群邮件的内容。 《Galois theory》 H.E. p. 57 (S43) * * * 15: 50 The essence of Galois' achievement was to determine the conditions imposed on the Galois group of an equation by the assumption that the equation is solvable by radicals . ---- 伽罗瓦的本 ...
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