Ib pawg sub ib txwm yog pawg sub uas yog invariant nyob rau hauv conjugation los ntawm txhua lub ntsiab ntawm pawg thawj: H yog ib txwm yog thiab tsuas yog g H g − 1=H gHg^ {-1}=H gHg−1=H. g \in G. Sib npaug, ib pawg H ntawm G yog ib txwm yog thiab tsuas yog tias g H=H g gH=Hg gH=Hg rau ib qho g ∈ G g / hauv G g∈G. …
Yuav ua li cas koj ua pov thawj ib pab pawg yog ib txwm?
Txoj hauv kev zoo tshaj los sim ua pov thawj tias ib pab pawg yog ib txwm ua kom pom tias nws txaus siab rau ib qho ntawm cov qauv sib npaug cov ntsiab lus ntawm normality
- Kab homomorphism muaj nws li kernel.
- Txheeb xyuas qhov tsis sib xws hauv qab automorphisms sab hauv.
- Txiav nws sab laug thiab sab xis cosets.
- Xaiv nws cov commutator nrog tag nrho pawg.
Yuav ua li cas hu ua ib pawg sub?
In abstract algebra, ib pawg sub (tseem hu ua invariant subgroup lossis self-conjugate subgroup) yog ib pab pawg uas tsis sib xws nyob rau hauv conjugation los ntawm cov tswv cuab ntawm pawg uas yog ib feem.
Vim li cas cov pab pawg ib txwm tseem ceeb?
Nyob ib pab pawg tseem ceeb vim lawv yog cov kernels ntawm homomorphisms. Hauv qhov kev nkag siab no, lawv muaj txiaj ntsig zoo rau kev saib cov qauv yooj yim ntawm pab pawg, ntawm pawg quotient.
Puas yog ib pawg ntawm pawg ib txwm muaj?
Feem ntau, ib pawg hauv nruab nrab ntawm ib pab pawg yog qhov qub. Nws tsis yog, txawm li cas los xij, qhov tseeb yog tias txhua pawg ntawm ib pab pawg yog qhov qub, ces pawg yuav tsum yog Abelian.
