現代数学の系譜工学物理雑談古典ガロア理論も読む77

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む77 (1002ﾚｽ)
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961: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/10/18(金) 07:18:10.93 ID:Zm+yHrIo

>>918
>・B_{5}'メタ巡回群 (位数 20)

追加参考
（後の”Metacyclic Group Wolfram MathWorld”の方が、綺麗に纏まっているが、書きぶりがちょっと違う）
https://en.wikipedia.org/wiki/Metacyclic_group
Metacyclic group
(抜粋)
In group theory, a metacyclic group is an extension of a cyclic group by a cyclic group. That is, it is a group G for which there is a short exact sequence
1 → K → G → H → 1
where H and K are cyclic. Equivalently, a metacyclic group is a group G having a cyclic normal subgroup N, such that the quotient G/N is also cyclic.
Properties
Metacyclic groups are both supersolvable and metabelian.
Examples
・Any cyclic group is metacyclic.
・The direct product or semidirect product of two cyclic groups is metacyclic. These include the dihedral groups and the quasidihedral groups.
・The dicyclic groups are metacyclic. (Note that a dicyclic group is not necessarily a semidirect product of two cyclic groups.)
・Every finite group of squarefree order is metacyclic.
・More generally every Z-group is metacyclic. A Z-group is a group whose Sylow subgroups are cyclic.

http://mathworld.wolfram.com/MetacyclicGroup.html
Metacyclic Group Wolfram MathWorld

http://rio2016.5ch.net/test/read.cgi/math/1568026331/961

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