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Paper   IPM / M / 17106
School of Mathematics
  Title:   On the multiplicities of the character codegrees of finite groups
1.  Zeinab Akhlaghi
2.  Mehdi Ebrahimi (Joint with M. Khatami)
  Status:   Published
  Journal: Algebr. Represent Theor.
  Year:  2023
  Pages:   DOI: 10.1007/s10468-022-10183-w
  Supported by:  IPM
Let G be a finite group and  be an irreducible character of G, the number cod() = jG : ker()j=(1) is called the codegree of . Also, cod(G) = fcod() j  2 Irr(G)g. For d 2 cod(G), the multiplicity of d in G, denoted by m′ G(d), is the number of irreducible characters of G having codegree d. A finite group G is called a T′ k-group for some integer k  1, if there exists d0 2 cod(G) such that m′ G(d0) = k and for every d 2 cod(G) 􀀀 fd0g, we have m′ G(d) = 1. In this note we characterize finite T′ k-groups completely, where k  1 is an integer.

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