Group Theory, Volume 1 |
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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 Example Exercise extension H factor group factor set field F 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 linear mapping matrix maximal subgroup natural number normal subgroup notation p-group permutation prime number Proof prove representation group S₁ semidirect product sequence Show simple groups SL(V solvable subgroup H subgroup of G subnormal series subset subspace Suppose Sylow's Theorem transvection u₁ uniquely determined v₁ vector space w₁ w₂ Weyl group wreath product