Group Theory, Volume 247Springer-Verlag, 1982 - Group theory |
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Results 1-3 of 81
Page 49
... Hence we have = po ( g ) = ( g ′′ ) " = gnm = ( g ′′ ) " = σp ( g ) . Thus , po and op map the generator g to the ... Hence there is an integer I such that ( g " ) ' = g . If G is infinite , we have nl 1. This implies that either n = 1 ...
... Hence we have = po ( g ) = ( g ′′ ) " = gnm = ( g ′′ ) " = σp ( g ) . Thus , po and op map the generator g to the ... Hence there is an integer I such that ( g " ) ' = g . If G is infinite , we have nl 1. This implies that either n = 1 ...
Page 295
... Hence , by ( 2.10 ) , A1 = NN1 , = N2 . NON { 1 } , and A , N × N ' . = In particular , | A | = | N | 2 . Then , n ≥ 5 and | N | is even . Hence , by Sylow's theorem , N contains an element σ of order 2. The cycle decomposition of o ...
... Hence , by ( 2.10 ) , A1 = NN1 , = N2 . NON { 1 } , and A , N × N ' . = In particular , | A | = | N | 2 . Then , n ≥ 5 and | N | is even . Hence , by Sylow's theorem , N contains an element σ of order 2. The cycle decomposition of o ...
Page 323
... Hence , ( D ) must be equal to D. Since D has exactly one vertex outside F , leaves every vertex of D invariant . Hence , for any E ≤ D , we have ø ( E ) = E. Similarly , we get ø ( ø ' ( E ) ) = E. This proves ( i ) . If C。= C ' we ...
... Hence , ( D ) must be equal to D. Since D has exactly one vertex outside F , leaves every vertex of D invariant . Hence , for any E ≤ D , we have ø ( E ) = E. Similarly , we get ø ( ø ' ( E ) ) = E. This proves ( i ) . If C。= C ' we ...
Common terms and phrases
a₁ abelian group additive group automorphism B₁ central extension Chapter cohomology commutator composition series conjugate Corollary corresponding cosets of H Coxeter group Coxeter system cyclic group defined definition denote direct product direct sum element g element of G elements of order endomorphism Example Exercise extension H factor group factor set finite group formula free abelian group free group function G-set G₁ GL(V group G group of order H₁ H₂ Hence Hint homomorphism induces integer irreducible isomorphic K₁ lemma Let F Let G Let H mapping matrix maximal subgroup natural number normal subgroup notation p-group permutation prime number Proof prove Q-invariant representation group S,-subgroup S₁ satisfies semidirect product sequence Show simple groups SL(V solvable subgroup H subgroup of G subset subspace Suppose Sylow's Theorem transvection u₁ uniquely determined v₁ vector space w₁ w₂ Weyl group wreath product