abstract algebra module 2, Lecture notes of Abstract Algebra

Download abstract algebra module 2 and more Lecture notes Abstract Algebra in PDF only on Docsity!

Proof ow ree Gr bea groups ok onder | pt. £ Gt Cee Cu - TE t fst then tHe ts abetion | Every uyebive group 1s Abel co | Now Suppose thet Cm i not cyelic the eves element m G& except 2° has enckrn P ! Leh a lee Such «=o element. the Lad bas ondty 9 omd go Sa> ~G. Lek beG suchthat 4 Lay. Men eb> has ender p We Con 5.7 24% 0 Z2b> =323 Th possible (ee ce Laroib>3CcH e then Ce Za> ond cé Zh> => Ler = L407 and Ley =eb> => Lar = Zb> This % not possilole : d So, we must hone Larqgdb> =Se3 By i sylow theorem , LOS ' 73° G@ notwal Sulbgtoup of a ‘gule qnoup Oo onder pr of G