feem ntau, cov khoom ntawm ob pawg S thiab T yog subgroup yog thiab tsuas yog ST=TS, thiab ob pawg sub yog hais kom permute.
Yuav ua li cas rau ib pab pawg Ib pawg?
A subset H ntawm pab pawg G yog ib pab pawg ntawm G yog tias nws tsis yog thiab kaw hauv qab cov khoom thiab hloov pauv . … Cov pab pawg neeg yog tus kheej ntawm pab pawg: yog G yog ib pab pawg uas muaj tus kheej eG, thiab H yog pab pawg G nrog tus kheej eH, then eH=eG.
Vim li cas kev sib tshuam ntawm ob pawg A subgroup?
Vim tsawg kawg yog lub cim qhia tus kheej 'e' yog ib txwm muaj rau H1 thiab H2. Vim H1 thiab H2 yog pab pawg. Yog li no, H1 ∩ H2 yog ib pab pawg ntawm G thiab qhov ntawd yog peb txoj kev xav piv txwv li kev sib tshuam ntawm ob pawg ntawm ib pab pawg rov qab ua pawg.
Puas yog cov khoom ntawm ob pawg pawg ib txwm muaj?
Subset Khoom ntawm Ib pawg Sub is Normal.
Puas yog union ntawm ob pawg sub yog ib pawg sub yog tsis muab piv txwv?
Yog ib pab G yog ib lub koom haum ntawm ob pawg H1 thiab H2, ces peb yuav tsum muaj H1⊄H2 thiab H2⊄H1, txwv tsis pub G=H1 lossis G=H2 thiab qhov no tsis tuaj yeem ua H1, H2 yog qhov tsim nyog. pab pawg. Ces G=H1∪H2 is a subgroup of G, txwv tsis pub part (a). Yog li, ib pab pawg twg tsis tuaj yeem yog ib lub koom haum ntawm pawg sub.