On B(4,14)Groups

Let G be a group and A be its n-element subset.The product set A2 is defined as{a1a2|a1,a2?A}.We say G is a B(n,k)group if |A2|?k where k?n2-1.B(2,k)groups and B(3,k)groups had been completely classified.As for B(4,k)groups,some scholars have given the complete classification of B(4,k)groups where k?13 recently.In this paper,we continue study B(4,14)groups.The thesis consists of four chapters.Chapter I is an introduction,which mainly introduces the research background,re-search methods and main results of this paper.Chapter ? gives a list of preliminaries,this section mainly introduces basic concepts,relative lemmas and conclusions to be used in this paper.Chapter III gives a complete classification of B(4,14)non-2-groups.Chapter IV mainly studys B(4,14)2-groups.In this chapter,we first give the classifications of some special B(4,14)2-groups and then get some simple properties of B(4,14)2-groups.