ΥڡϤƤʥ֥åޡɲΥڡޤϤƤʥ֥åޡ Υڡlivedoor åפɲΥڡޤlivedoor å

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(G,~\circ)ϷǤȤ롣
GʬG'GƱ黻\circ˴ؤƷˤʤäƤȤ(G',\circ)뤤ñG'GʬsubgroupǤȤ[1]

ǡGG'α黻ƱȤȤڤǤ롣ñƱα黻ȤäƤǤϤʤG'ˤa~\circ~b~=~cǤȤΤϡGˤƤǤa~\circ~b~=cȤʤäƤȤǤ롣

1Gˤơ{e}ñ̸ΤߤʬˤGGȡˤʬǤ롣

ɤΤ褦ʷˤƤΩĤΤǡ2ĤʬȸƤФ롣

2(Z,+)Фơ({3x|xZ},+)ʬǤ롣

3(G,~\circ)ʬ(G_1,~\circ)(G_2,~\circ)Ȥ(G_1~\cap~G_2,~\circ)GʬǤ롣

(G_1~\cup~G_2,~\circ)GʬȤϸ¤ʤ

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[]GζǤʤʬSGʬǤɬ׽ʬϼξΤ1Ĥ­뤳ȤǤ[1]
(i)\forall~x,y~\in~S;~x~\circ~y^{-1}~\in~S
(ii)\forall~x,y~\in~S;~x^{-1}~\circ~y~\in~S

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  • [1]ؾʳؤΤ4ϡ3ηˡpp.57-67