On the Kernel of Restriction of Characters

Abstract

Let G be a finite group, H be a proper subgroup of G, and S be a unitary subring of C. The kernel of the restriction map S[Irr(G)] → S[Irr(H)] as a ring homomorphism is studied. As a corollary, the main result in [Isaacs, I. M. and Navarro, G., Injective restriction of characters, Arch. Math., 108, 2017, 437–439] is reproved.

Keywords

Characters / Character ring / Character restriction

References

[1] Chen G, Fan Y. On the connected components of the spectrum of the extended character ring of a finite group. J. Algebra, 2007, 312: 689-698

[2] Isaacs I M. Character Theory of Finite Groups, 2006, Providence, Rhode Island: AMS Chelsea

[3] Isaacs I M. Finite Group Theory, 2008, Providence, Rhode Island: American Mathematical Society

[4] Isaacs I M, Navarro G. Injective restriction of characters. Arch. Math., 2017, 108: 437-439

[5] Ferguson P, Isaacs I M. Induced characters which are multiples of irreducibles. J. Algebra, 1989, 124: 149-157

[6] Serre J P. Linear Representations of Finite Groups, 1977, Beijing: Springer-Verlag, World Publishing Corporation