Character Theory of Finite Groups
Courier Corporation, 1 jan 1994 - 303 pagina's
Excellent text approaches characters via rings (or algebras). In addition to techniques for applying characters to "pure" group theory, much of the book focuses on properties of the characters themselves and how these properties reflect and are reflected in the structure of the group. "A pleasure to read." — American Mathematical Society. 1976 edition.
Algebras modules and representations
Group representations and characters
Characters and irttegrality
Products of characters
TI sets and exceptional characters
Changing the ﬁeld
The Schur index
Changing the characteristic
Overige edities - Alles bekijken
Character Theory of Finite Groups: Conference in Honor of I. Martin Isaacs ...
Mark L. Lewis
Gedeeltelijke weergave - 2010
9 is extendible afforded algebraic integer Brauer character CG(x character of G character table character theory character triple class function classes of G conclude conjugacy classes conjugate COROLLARY Let coset cyclic defined elements exists F-algebra F-representation of G F[G]-module finite Frobenius group G and let G is solvable Galois group G hence Hint Let homomorphism IBr(G induction invariant in G Irr(C Irr(H Irr(K Irr(N irreducible characters irreducible constituent irreducible F-representation isomorphism LEMMA Let Let 9 Let G Let H Let xe Irr(G linear character linear group matrix module nilpotent nonabelian normal subgroup Note p-block p-group permutation prime Problem projective representations proof is complete Proof Let prove result follows root of unity S-invariant Show that G splitting field subgroup of G Suppose Sylow p-subgroup THEOREM Let theory unique write yields