The Classification Of Finite 2-groups Which Have At Least One Abelian Maximal Subgroup Generated By Two Elements

Assume F is a cyclic group. If there is a group G which has a normalsubgroup N such that G/N=～F , then G is called a cyclic extension of Nby F. In this paper, we completely classify finite 2-groups which have atleast one abelian maximal subgroup generated by two elements by meansof a cyclic extension.This paper consists of four chapters. ChapterⅠis an introductionto this paper. ChapterⅡgives a list of preliminaries for this paper. InChapterⅢ, we give the conjugate classes of involutions of Aut(C_2n×C_2m).In ChapterⅣ, we classify finite 2-groups which have at least one abelianmaximal subgroup generated by two elements.