Ib pawg dawb yog ib pawg residually finite group , i.e., rau txhua qhov tsis yog tus kheej ntawm ib pab pawg dawb, muaj ib pawg subgroup ib txwm subgroup Ib pawg sub ntawm ib txwm subgroup ntawm ib pab pawg xav tau not ua ib txwm nyob hauv pab pawg. … Cov pab pawg tsawg tshaj plaws uas nthuav tawm qhov tshwm sim no yog pawg dihedral ntawm kev txiav txim 8. Txawm li cas los xij, ib pab pawg neeg ntawm ib pab pawg ib txwm muaj. Ib pawg uas normality yog transitive yog hu ua T-group. https://en.wikipedia.org › wiki › Normal_subgroup
Ntau pab pawg - Wikipedia
ntawm qhov ntsuas qhov kawg hauv tag nrho pawg tsis muaj cov ntsiab lus.
Puas yog pawg finite?
A finite group is a group muaj finite group order. Piv txwv ntawm finite pawg yog cov modulo multiplication pawg, point pawg, cyclic pawg, dihedral pawg, symmetric pawg, alternating pawg, thiab hais txog.
Puas yog ib pab pawg tsim tawm finite?
Los ntawm txhais, txhua pawg finite yog finitely generated, vim S tuaj yeem coj los ua G nws tus kheej. Txhua pab pawg uas tsim tsis kawg finitely yuav tsum suav tau tab sis suav tau pab pawg tsis tas yuav tsim kom tiav. Cov pab pawg ntxiv ntawm cov lej muaj txiaj ntsig Q yog ib qho piv txwv ntawm pawg suav tau uas tsis raug tsim tawm.
Koj ua pov thawj pab pawg li cas?
Yog G yog ib pab neeg finite, txhua g ∈ G muaj finite order Cov pov thawj yog raws li nram no. Txij li cov txheej txheem ntawm lub hwj chim {ga: a ∈ Z} yog ib feem ntawm G thiab cov exponents ib tug khiav ntawm tag nrho cov integers, ib infinite set, yuav tsum muaj ib tug repetition: ga=gb rau ib co a<b nyob rau hauv Z. Ces gb−a=e, yog li g tau txiav txim siab kawg.
pab pawg twg hu ua pawg seem?
Piv txwv. Piv txwv ntawm cov pab pawg uas tsis muaj qhov kawg yog cov pab pawg tsis kawg, pab pawg pub dawb, cov pab pawg tsis muaj zog tshaj plaws, cov pab pawg polycyclic-los-finite, finitely generated linear pawg, thiab cov pab pawg tseem ceeb ntawm compact 3-manifolds.
