Finite Groups Having Monolithic Characters of Prime Degree
Abstract
Let G be a finite group. An irreducible character χ is called monolithic when the factor group G/ker(χ) has unique minimal normal subgroup. In this paper, we prove that for the smallest prime q dividing the order of G if G has a faithful imprimitive monolithic character of degree q, then G becomes a nonabelian q-group or a Frobenius group with cyclic Frobenius complement whose order is q. Under certain conditions, we also classify finite groups in which their nonlinear irreducible characters are monolithic.
Keywords
Finite groups, Monolithic characters, Primitive characters
Project Number
References
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