Group Structure on Cantor p-ary sets

โครงสร้างกรุปบนเซต-พีอารี คันทอร์

Name: Riduan Waema

Organization : Prince of Songkla University, Pattani Campus Faculty of Science and Technology

keyword: Cantor set

; เซตคันทอร์

Abstract: The Cantor set or the Cantor middle thirds set was constructed by Georg Cantor (Nelson, n.d. ). In this thesis, we define the generalization of the Cantor set namely Cantor -ary set , where is an odd prime. Then we give the definitions of spawning -ary set and child -ary sets , where This thesis consists of two parts. The first part, we prove the relation of cardinality of spawning -ary set and child -ary set , that is where . The second part, we define a transformation by swapping a digit with its complement and denote a transformation by cycle the digit in to the left. Then we construct a group which its elements are generated by the transformation and transformation and we prove that where is an identity function and be the period length of elements in spawning -ary sets and commute is isomorphic to the subgroup generated by alone, is a faithful cyclic subgroup of order Moreover, we prove that and

Abstract:

Prince of Songkla University, Pattani Campus. Office of Academic Resources

Address: PATTANI

Email: oar.psu@gmail.com

Name: Aniruth Phon-On

Role: Advisor

Created: 2016

Modified: 2561-05-15

Issued: 2018-05-15

วิทยานิพนธ์/Thesis

application/pdf

eng

DegreeName: Master of Science

Level: Master's Degree

Descipline: Applied Mathematics

Grantor: Prince of Songkla University, Pattani Campus

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