SageMath version 9.0, Release Date: 2020-01-01
Using Python 3.8.5. 
Ubuntu 20.04 LTS 
64bit

Hi,

I want to create the multiplicative group (Z/7Z)*={1,2,3,4,5,6}

I did these steps:

sage: 
n=7                                                                             
              
 

sage: 
Zn=Zmod(n)                                                                      
              
 

sage: G=Zn.unit_group()  

sage: list(G) 

[1, f, f^2, f^3, f^4, f^5]                                                      
              


sage: 
G.inject_variables()                                                            
              
 
Defining f

Then I want to create the subgroups H generated by f^2=2 mod 7 which is {1,2
,4}.

I did the following steps:
sage: H = 
G.subgroup([f^2])                                                               
          
 

sage: 
list(H)                                                                         
              
 

[1, f, f^2]

sage: 
Zn(f)                                                                           
              
 

3

"There seems to be a bug in the subgroup method: H should consist of [1, 
f^2, f^4]."
 cf:
https://ask.sagemath.org/question/57703/how-can-i-manipulate-a-multiplicative-group-of-zmodn/

Is there a solution for this ? Or I miss something?


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