The basis of a subgroup H⊂Z4

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manpreet Tuteehub forum best answer Best Answer 2 years ago

Dear fellow mathstack exchangers,

There is a question in my Abstract Algebra syllabus I have trouble with solving, the main problem is is that there is no clear description of the algorithm I need. Sorry for my lack of initiative, but I don`t know where to start. Here is the question:

Find the basis for the subgroup HZ4H⊂Z4, given by

H={(a,b,c,d)a+b+c+d=0   and  ac  (mod12)}H={(a,b,c,d)∣a+b+c+d=0   and  a≡c  (mod12)}

 

Thank you for the help!

PS: This is my first mathstack exchange post

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