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Chillag, D. and Herzog, M. (1990) On the Length of the Conjugacy Classes of Finite Groups. Journal of Algebra, 131, 110-125.
https://doi.org/10.1016/0021-8693(90)90168-n

has been cited by the following article:

• TITLE: Note on Finite Groups Possessing a Normal Series with Factors of Sub-Class Size 1

  AUTHORS: Qi Liang, Yanheng Chen, Jiawei Li

  KEYWORDS: Finite Groups, Sub-Class Sizes, Factor Group, Solvable Group

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.11, November 5, 2026

  ABSTRACT: For a finite group G and any x∈G , G x is defined to be the unique minimal subnormal subgroup of G that contains the element x . The conjugacy class of x in G x is called the sub-class of x in G , and its size is called the sub-class size of x in G . This note mainly investigates finite groups that admit a normal series in which every factor group has sub-class size 1. It is proved that if each factor group of some normal series of a finite group G has sub-class size 1, then G is solvable. Conversely, if G is solvable, then there exists a normal series of G such that each of its factor groups has sub-class size 1. In particular, G is a solvable group if and only if each chief factor of G has sub-class size 1.