Endliche Gruppen, Volume 2 |
Contents
Elements of General Representation Theory | 1 |
Extension of the GroundField | 4 |
Splitting Fields | 27 |
Copyright | |
35 other sections not shown
Common terms and phrases
A-module a₁ Abelian group absolutely indecomposable absolutely irreducible algebraically closed assertion associative algebra automorphism b₁ char commutative completely reducible composition factor cyclic decomposition defined direct sum direct summand divides divisor elementary Abelian epimorphism exists exponent Fermat prime field of characteristic finite dimension finite group follows at once free associative algebra G₁ GF(p group-ring H₁ Hence homomorphism ideal of g idempotents indecomposable KG-module indecomposable projective inductive hypothesis integer irreducible KG-module isomorphic J(KG K-basis KG-module KG-submodule L₂ Lemma Let G Lie algebra Lie ring mapping Math minimum polynomial module n₁ nilpotent non-singular non-zero normal subgroup operates trivially p-group p-length p-soluble group P₁ P₂ permutation prime projective KG-module Proof representation right ideals S₁ soluble splitting field subalgebra submodule Suppose that G Sylow p-subgroup symplectic Theorem U₁ V₁ V₂ vector space W₁ W₂ X₁ y₁