臺灣博碩士論文加值系統

在這一篇文章中,我們考慮群擴張問題. 為了處理這個問題,我們用了在同調代數中的群擴張理論. 此外,我們還明確的寫出所有的2-cocycle.

In this paper, we discuss the extensions of (Zp)^r
by Zp for arbitrary rЄN. belonging to natural number. In order to deal with this problem, we use the theory
of group extensions, which is a beautiful application of group cohomology. Furthermore, we also exhibit 2-cocycles in C^2((Zp)^r, Zp) explicitly.

Introduction 1
Preliminaries 2
Group Extension 5
Computation of H^q((Z_p)^r, Z_p) 11
Explicit Computation of 2-cocycles in C^2(((Z_p)^r, Z_p) 20
Classification of Extensions of (Z_p)^r by Z_p 24
References 26

K. S. Brown, Cohomology of Groups, GTM 74, Springer-Verlag.

Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo and Mucheng Zhang, Cohomology rings of finite groups, Kluwer Academic Publisher, Dordrecht, 2003.

David S. Dummit and Richard M. Foote, Abstract
Algebra 2nd. ed. John Wiley & Sons,Inc.

Suichi Takahashi, Cohomology Groups of Finite Abelian
Groups, Tôhoku Math. J. 4,(1952). 294-302.