19/06/25 00:24:45.92 Z88Lzyyd.net
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スレ70 ｽﾚﾘﾝｸ(math板:890番)
＞ガロア第一論文の第八節の分り易い説明は、探しています
分り易いとは言えないかもしれないが、下記が纏まっていると思う（＾＾
検索：ax+b p(p-1) solvable group garois affine OR linear
で下記ヒット
URLﾘﾝｸ(core.ac.uk)
JOURNAL OF NUMBER THEORY 24, 305-359 (1986)
Polynomials with Frobenius Groups
of Prime Degree as Galois Groups II
AIDEN A. BRUEN*
CHRISTIAN U. JENSEN
NORIKO YUI *
(抜粋)
P309
I. CHARACTERIZATION THEOREMS OF POLYNOMIALS WITH FROBENIUS GROUPS OF PRIME DEGREE AS GALOIS GROUPS
I. 1. Preliminary Results
The structure of a Frobenius group G of prime degree p >= 5 is described by a theorem of Galois.
LEMMA (1.1.1). Let G be a transitive permutation group of prime degree p >= 5.
Then the following conditions are equivalent:
(i) G has a unique p-Sylow subgroup.
(ii) G is solvable.
(iii) G is identified with a subgroup of the group of one-dimensional affine transformations
on Fp : Aff(Fp) = {x→cx + d ｜ d∈Fp, c ∈ Fp*}.
(iv) G is a Frobenius group of degree p.
Proof See, e.g., Huppert [12, p. 163].
(引用終り)
URLﾘﾝｸ(en.wikipedia.org)
Frobenius group
(抜粋)
Examples
For every finite field Fq with q (> 2) elements,
the group of invertible affine transformations
x → ax+b, a≠0 acting naturally on Fq is a Frobenius group.