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II : bustling :i Galois theory ) ( Fundamental Theorem of Thur - - PowerPoint PPT Presentation

Sep 10, 2022 •21 likes •111 views

Fundamental Theorem worked examples II : bustling :i Galois theory ) ( Fundamental Theorem of Thur - ids.ba , The and f satisfy A. F F functions - ::i:: Galois ift Ciii ) KIF Alk ) of is iff FIH )

  1. Fundamental Theorem worked examples II :

  2. bustling :i÷÷÷ Galois theory ) ( Fundamental Theorem of Thur - ids.ba , The and f satisfy A. F F functions - ÷÷÷÷÷÷:÷:÷i÷:÷:÷÷÷÷÷ Galois ift Ciii ) KIF Alk ) of is iff FIH ) Ip Civ ) Galois . HOG is

  3. Y " fundamental the Use to explore Sean theorem familiar examples

  4. computed EI Consider We've EHR . = Eide , Gayle complex conjugation : - bi That bi ) = a i÷÷÷÷÷÷÷÷

  5. be splitting field for - 2e HI . x3 we've seen EI let E rt Gulf El ) acting element , with Gal ( E/ ④ ) a- Sz as an w 't } { Vz , wVz , of symmetric group an % L2 L , i :i÷÷ : lid ) E ④ ✓ S3 are only intermediate µ .ge extent " " ! Sub ( G ) Lat LEI )

  6. isomorphism the Should c Gall Ela ) ? be 112 ) What is - sends that > az a , t Lz ( → a £31463 : fir ) F- ( cans ) ? Okla ) what is So : ÷ Okla ) Flash ) ? - ka Similarly - : 9- Kay 14g ? ÷÷¥÷÷ : 's ) ? ⇒ out - w wut is

  7. Gall KIF ) ' En Exe suppose . precisely subgroups of kn are Recall : d , where d of is size cyclic subgroups divisor of Moreover , positive n . a get , then we H . . Ha E kn if t Hill that iff A. a- Hz . " dual " Lat ( KIF ) Galois they have is By , we structure . this te

  8. 12.3.46 , 12 ) Gul ( KH ) E 742 if ( divisors So : are - { e ) , Hu - G H , corespewdj subgroups - . . . :÷÷÷÷÷i÷ let it Lat ( KIF ) Sub (G)

  9. observation special One : lattices ) finite extensions have Cod ( Galois that CKIFH so then Galois is If KIF . , bijection in Lat ( KIF ) are of PI Elements , and at Gallerie ) we subgroups with ' - F ) 214144Mt . 28k at most have . subgroups DM .

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