Group Theory, Volume 247Springer-Verlag, 1982 - Group theory |
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