On Induced Characters
Copyright policy )On Induced Characters
Suppose that H is a normal subgroup of a finite group G, φ ∈ Irr ( H ) \varphi \in {\text {Irr}}(H) , and Irr ( φ G ) {\text {Irr}}({\varphi ^G}) is the set of all irreducible constituents of the induced character φ G {\varphi ^G} . If | Irr ( φ G ) | > | G : H | / 4 |{\text {Irr}}({\varphi ^G})| > |G:H|/4 then G / H G/H is solvable.
Ordinary representations and characters, normal subgroups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, irreducible characters, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, irreducible constituents, Arithmetic and combinatorial problems involving abstract finite groups, finite groups, solvable groups
Ordinary representations and characters, normal subgroups, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, irreducible characters, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, irreducible constituents, Arithmetic and combinatorial problems involving abstract finite groups, finite groups, solvable groups
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