| In the finite group,group order and element order have great influence to the structure of group.We can get the structure of group by research order of the group and element order.In 1984,Wujie Shi proved that the alternating group A5 can be determined uniquely by its order and the all orders of elements.Basing on this ideal,we use group order and the class number of same order to study the structure of some groups,and obtain the following two results:1.The all groups of order 2qp are studied.We get the minimum value of the numbers of same order element classes,and the structure of groups of order 2qp with the minimum class number of same element order.2.For（1）p≠3,7,（2）p=7,（3）p=3,the minimum value of the numbers of same order element classes of groups of order 8p is respectively given,and the structure of groups of order 8p with the minimum class number of same element order.This paper is divided into the following four sections to introduce the main content:In section one:we introduce some backgrounds of our research.In section two:we introduce some basic definition and lemmas.In section three:we introduce the structure of groups of order 2qp with the minimum class number of same element order.In section one:we introduce the structure of groups of order 8p with the minimum class number of same element order. |
