The study of the centralizer of idempotent transformation
Specialty：Information and Computing Science
Student: Gong Chao
Advisor: Tian Jing
ABSTRACT
For a nonempty subsetof .We call the set
the centralizer of S.
Let X be a set and an equivalence relation on X. A subset of is called a -cross-section provided that R contains exactly one representative from each equivalence class.
Let be an idempotent transformation with kernel and image .It has been proved in literature [1] that
is the centralizer of .
In this paper, we focus on the set and determine the order of in chapter 2. Also, in chapter 3, we compute the number of the permutation in the set that is the order of the set，where
.
Key words: Idempotent transformation, Centralizer, Order, Permutation group
