Nyob rau hauv lej, ib pab pawg neeg abelian, kuj hu ua ib pawg pab pawg sib tham, yog ib pab pawg uas tshwm sim los ntawm kev siv pab pawg ua haujlwm rau ob pawg ntsiab lus tsis nyob ntawm qhov kev txiav txim. uas lawv sau.
Dab tsi yog pawg neeg Abelian thiab tsis yog Abelian?
Definition 0.3: Pawg Abelian Yog ib pab pawg muaj cov cuab yeej uas ab=ba rau txhua khub ntawm cov ntsiab lus a thiab b, peb hais tias pawg yog Abelian. Ib pawg tsis yog-Abelian yog tias muaj qee cov ntsiab lus a thiab b uas ab=ba.
Koj paub li cas pab pawg neeg abelian?
Txoj Kev Qhia Ib Pawg yog Abelian
- Show the commutator [x, y]=xyx−1y−1 [x, y]=x y x − 1 y − 1 of two arbitary elements x, y∈G x, y ∈ G yuav tsum yog tus kheej.
- Qhia cov pab pawg isomorphic rau cov khoom ncaj qha ntawm ob pawg abelian (sub).
Dab tsi yog qhov txawv ntawm pab pawg thiab pawg neeg abelian?
Ib pawg yog ib pawg nrog ib yam khoom thiab tag nrho cov morphisms invertible; ib pawg abelian yog ib pawg monoidal nrog ib qho khoom thiab tag nrho cov morphisms invertible.
Pab pawg twg ib txwm yog abelian?
Yes, tag nrho pawg cyclic yog abelian. Nov yog qee qhov kev nthuav dav ntxiv uas pab ua kom pom tseeb tias "vim li cas" txhua pawg cyclic yog abelian (piv txwv li kev sib txuas lus). Cia G ua ib pab pawg thiab g ua generator ntawm G.
