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88 sonuçtan 1-3 arası sonuçlar
Sayfa 210
PROOF OF THEOREM 6 . 1 We shall show that ( 2 ) = ( 1 ) = ( 3 ) = ( 2 ) . To prove
the implication ( 2 ) 3 ( 1 ) , suppose that W , = Z ( K , G ) with K < Aut ( G ) .
Obviously , the stabilizer of any generator of G in the group K is trivial . Therefore ,
K is ...
PROOF OF THEOREM 6 . 1 We shall show that ( 2 ) = ( 1 ) = ( 3 ) = ( 2 ) . To prove
the implication ( 2 ) 3 ( 1 ) , suppose that W , = Z ( K , G ) with K < Aut ( G ) .
Obviously , the stabilizer of any generator of G in the group K is trivial . Therefore ,
K is ...
Sayfa 215
4 . The following statements are true : ( 1 ) A E H ( A ) and AA = O ( K , A ) ; ( 2 ) if
Xe S ( A ) , then pro ( X ) , pra ( X ) E S ( A ) . Proof . For x E F , let n ( x ) = r . 1€T .
First , we prove that for any primitive element g of F we have ( 41 ) Y - 1Xntx - lYt ...
4 . The following statements are true : ( 1 ) A E H ( A ) and AA = O ( K , A ) ; ( 2 ) if
Xe S ( A ) , then pro ( X ) , pra ( X ) E S ( A ) . Proof . For x E F , let n ( x ) = r . 1€T .
First , we prove that for any primitive element g of F we have ( 41 ) Y - 1Xntx - lYt ...
Sayfa 216
We prove statement ( 1 ) . Let a E F be such that lag e Orb ( K , I ) . It suffices to
show that sa · gP ] E Orb ( K , ) . However , since ( 0 . gʻ ) e Orb ( K , G ) for all i ,
we have ( 42 ) [ 0 . 9P - ] [ a · g ] n A [ 0 . 99 ] = { a · ( 9P - 1 ) og ? : ( gP - 1 ) og ?
We prove statement ( 1 ) . Let a E F be such that lag e Orb ( K , I ) . It suffices to
show that sa · gP ] E Orb ( K , ) . However , since ( 0 . gʻ ) e Orb ( K , G ) for all i ,
we have ( 42 ) [ 0 . 9P - ] [ a · g ] n A [ 0 . 99 ] = { a · ( 9P - 1 ) og ? : ( gP - 1 ) og ?
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algebraic analytic apply assume basis boundary bounded called chain homotopy closed coefficients complex computation condition connection Consequently consider constant construction contains continuous convex corresponding defined definition deformation denote determined differential domain element equal equation equivalence estimate example exists extension fact field finite fixed formula function given identity implies inequality integral intersection introduce invariant inverse isomorphism Lemma linear Math Mathematical matrix measure metric Moreover natural normal Observe obtain Obviously operator orientation particular periodic positive present problem projective Proof properties Proposition prove regular relation Remark respectively result ring satisfies scheme sequence singular smooth solutions space standard statement Subsection suffices Suppose takes Theorem theory transformation true twists unique vector weight zero