Characters of Finite Groups, Volume 2
This book places character theory and its applications to finite groups within the reach of people with a comparatively modest mathematical background. The work concentrates mostly on applications of character theory to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations of monomial groups. The presentation is detailed, and many proofs of known results are new.
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7r-Hall subgroup abelian subgroup Algebra assume that G assumption cd G CG(x Chapter character of degree characters of G Classify Clifford's Theorem complement conjugacy classes conjugate in G cyclic denote Di-group divides G divides x(l divisor of G elementary abelian elements epimorphic epimorphic image Exercise faithful character faithful irreducible character finite groups Frobenius group G contains G is p-nilpotent G is solvable G-classes group G group of order group with kernel Hall subgroup implies integer involutions isomorphic kerx Let G Let H Let x e Lin(G Maschke's Theorem minimal normal subgroup natural numbers NG(P nilpotent nonabelian group nonabelian simple groups nonlinear irreducible characters nonsolvable normal p-complement Obviously odd order p-group permutation prime divisor Proof Proposition prove representation result semidirect product solvable group splitting field subgroup of G subgroup of order Suppose that G Sylow p-subgroup Sylp(G unique minimal normal x e Irr(G Zsigmondy prime