On the multiplicities of the character codegrees
Zeinab Akhlaghi, Mehdi Ebrahimi, Maryam Khatami

TL;DR
This paper characterizes finite groups where all but one codegree have multiplicity one, and the remaining codegree has a specified multiplicity, providing a complete classification of such groups.
Contribution
It offers a complete characterization of finite $T'_k$-groups, expanding understanding of the structure of groups based on codegree multiplicities.
Findings
Characterization of finite $T'_k$-groups for all $k \\geq 1$
Identification of the unique codegree with multiplicity greater than one
Complete classification of groups with prescribed codegree multiplicity patterns
Abstract
Let G be a finite group and ? be an irreducible character of G, the number cod(?) = jG : Let be a finite group and be an irreducible character of , the number is called the codegree of . Also, . For , the multiplicity of in , denoted by , is the number of irreducible characters of having codegree . A finite group is called a -group for some integer , if there exists such that and for every , we have . In this note we characterize finite -groups completely, where is an integer.
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · graph theory and CDMA systems
