現代数学の系譜工学物理雑談古典ガロア理論も読む78

現代数学の系譜工学物理雑談古典ガロア理論も読む78at MATH

現代数学の系譜工学物理雑談古典ガロア理論も読む78 - 暇つぶし2ch141: subgroups of permutation groups are true for groups in general. Nevertheless, Alperin and Bell note that "in general the fact that finite groups are imbedded in symmetric groups has not influenced the methods used to study finite groups".[4] The regular action used in the standard proof of Cayley's theorem does not produce the representation of G in a minimal-order permutation group. For example, {\displaystyle S_{3}}S_{3}, itself already a symmetric group of order 6, would be represented by the regular action as a subgroup of {\displaystyle S_{6}}S_{6} (a group of order 720).[5] The problem of finding an embedding of a group in a minimal-order symmetric group is rather more difficult.[6][7] (引用終り) 以上

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