Assignment - Project Synergy

 

Classification of finite Abelian groups

 

 

Course: Abstract Algebra course

Made by: Palanivel Manoharan (UMUC)

 

Web site used: http://www.d.umn.edu/~jgallian/msproject/chap11.html

 

Objective: To understand the classification of finite Abelian groups

 

The software at this web site,

1.      Lists the isomorphism classes of finite Abelian groups of any given order,

2.      Determines how many integers in a given interval are the order of exactly from one up to nine Abelian groups, and

3.      Expresses a finite Abelian group of prime power order as an internal direct product of cyclic groups.

 

Assignment:

Visit the web site http://www.d.umn.edu/~jgallian/msproject/chap11.html and calculate the following:

 

1.      Find the isomorphism classes of finite Abelian group of order n.  Run the program for any five integers less than 1,000,000.

2.      Choose an interval of 1000 consecutive integers and find out exactly how many integers are the orders of exactly from one up to nine Abelian groups.

3.      Find the internal direct product of U(32), U(65) and U(80).