what is distinct cyclic subgroup? Does it mean A4 = {1,2,3,4} ?
to find all of the subgroup, should it be: (1,2,3,4) , (2,1,3,4) , ( 1,2,4,3) etc ... or it should be (1,2) , (1,3), (1,4) ???
what is distinct cyclic subgroup? Does it mean A4 = {1,2,3,4} ?
to find all of the subgroup, should it be: (1,2,3,4) , (2,1,3,4) , ( 1,2,4,3) etc ... or it should be (1,2) , (1,3), (1,4) ???
I hope you know that where . And then a cyclic subgroup of would be a subgroup that is generated by one element. What's the problem?
since you said "then a cyclic subgroup of would be a subgroup that is generated by one element." Would that mean the answer is simply {(1), (2), (3), (4)} there are 4 distinct cyclic subgroups?
since you said "then a cyclic subgroup of would be a subgroup that is generated by one element." Would that mean the answer is simply {(1), (2), (3), (4)} there are 4 distinct cyclic subgroups?
Whose to say those are all distinct? I mean you could cover all of the cyclic subgroups of in the class but you wouldn't know which are distinct.
since you said "then a cyclic subgroup of would be a subgroup that is generated by one element." Would that mean the answer is simply {(1), (2), (3), (4)} there are 4 distinct cyclic subgroups?
List the different order out, and then find the cyclic subgroup. If you see any of them have the same cyclic subgroup, then just take one of them.