Linear Representation of Finite Groups, Issues 5-6 |
Contents
Preliminaries on Finitely Generated Modules | 12 |
Torsion Modules | 24 |
Structure of Finitely Generated Modules | 35 |
Copyright | |
7 other sections not shown
Common terms and phrases
abelian group algebraic integer algebraically closed field artinian ring assume canonical matrix character coefficients completely reducible A-module complex numbers cyclic group decomposition defined by setting denote diagonal diagonalizable dimension direct sum distinct divides elementary divisors finite group finite number finitely generated modules follows group G hence hermitian form indecomposable invariant factors invertible involution irreducible A-module irreducible polynomials irreducible representations isomorphic K-basis K-space K[X]-module KG-module left ideal left-ideal lemma linear representation linear transformation mapping matrix representation minimal left ideal minimal polynomial Moreover nilpotent non-trivial non-zero one-to-one orthogonal pairwise permutation polynomial q prime element prime number principal ideal domain Proof proposition prove quotient R/Rp representation of G representation space roots of unity semi-simple ring sesquilinear form skewfield subgroup of G submodule subspace theorem torsion-free trivial two-sided ideal uniquely vector space