Speaker Introduction

Mr. Wang Kah Lun is a Lecturer at Xiamen University Malaysia, and he was Graduate Research Assistant at the University of Malaya. Moreover, he was Lecturer at Methodist College Kuala Lumpur, and his PhD is expected to be defended in this year 2023.

Abstract

Let G be a group and letA1, . . . , Ak(k≥2)be nonempty subsets of G. The sequence[A1, . . . , Ak]is called a complete decomposition of Gif the productA1···Ak is equal to G and the setsA1, . . . , Ak are mutually disjoint. The integer and the sum∑ki=1|Ai|are called the order and size of[A1, . . . , Ak], respectively. A complete decomposition [A1, . . . , Ak] of G is said to be a complete factorization of G if every element of G can be uniquely expressed as a product of the forma1···ak with ai∈ Ai for each i= 1, . . . , k.  In this talk, we discuss the existence of complete decompositions of groups. We also discuss the structure of groups that have a complete decomposition satisfying certain conditions.  In addition, we discuss the possible orders and sizes for complete decompositions of a group.  Next, we discuss necessary and sufficient conditions for a finite abelian group to have a complete factorization. Department of Mathematics and Applied Mathematics, Xiamen University Malaysia.