Some Results on the Linear Groups |
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Page 14
... Proof : n - 1 n - 2 . Suppose not . Let r be the largest value for which there exists an a ‡ identity in HK . Then α ... Proof : Gierster [ 4 ] , pages 332 and 333 . = p and H is a subgroup Proposition 1.3 . The largest cyclic subgroup ...
... Proof : n - 1 n - 2 . Suppose not . Let r be the largest value for which there exists an a ‡ identity in HK . Then α ... Proof : Gierster [ 4 ] , pages 332 and 333 . = p and H is a subgroup Proposition 1.3 . The largest cyclic subgroup ...
Page 22
... proof . Proposition 1.6 . Suppose HK is cyclic . Then HK is cyclic n - 1 n - r for r = 1 , n- 1 . Proof : The proof is by induction on r . Since we know that HOK is n - 1 cyclic , we suppose Hok n - r = is cyclic and show that HOK [ U ] ...
... proof . Proposition 1.6 . Suppose HK is cyclic . Then HK is cyclic n - 1 n - r for r = 1 , n- 1 . Proof : The proof is by induction on r . Since we know that HOK is n - 1 cyclic , we suppose Hok n - r = is cyclic and show that HOK [ U ] ...
Page 37
... Proof : If F is not a subfield of K ( 25 ) , then H does not contain K3 and so | H ^ K3 | = 1 , 5 or 25. If | H ^ K3 | = 1 or 5 , then , as in lemma 2.14 , | □ ¬K } | H proposition 1.1 or 1.3 . If HK3 | = 25 or 125 respectively which ...
... Proof : If F is not a subfield of K ( 25 ) , then H does not contain K3 and so | H ^ K3 | = 1 , 5 or 25. If | H ^ K3 | = 1 or 5 , then , as in lemma 2.14 , | □ ¬K } | H proposition 1.1 or 1.3 . If HK3 | = 25 or 125 respectively which ...
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25 elements assume belongs calculate chapter choices classes compute congruence subgroup conjugate consider contradicting proposition 1.1 cyclic defined denote describes all values determinant divides elements of order equal example exists F₁ fact field Finally fixed function fundamental domain Further genus Gierster pages given gives group of order H contains H has order H is conjugate H^K² H₁ Hence ideal identity implies induction integer Klingenberg Lemma linear matrix normal subgroup notation Note obtain order 12 order 36 particular positive possibilities Proof proposition 1.5 residue mod respectively ring Sp(L subfield of K(27 subgroup of H subgroup of Sp(R subgroups H subgroups of order Suppose F Sylow tables Theorem thesis transformations unit values mod 9 yield zero