The problem involves identifying and describing all the subgroups of the groups Z/9Z and Z/3Z x Z/3Z, including determining the number of such subgroups.
Participants are sharing their attempts and seeking validation of their reasoning. There is an ongoing exploration of subgroup structures, with some guidance being offered regarding the elements of Z/9Z and the nature of Z/3Z x Z/3Z.
There appears to be a lack of clarity regarding the definitions and properties of the groups involved, as well as the specific requirements for describing the subgroups.
porroadventum said:I have made an attempt, if someone could let me know if it is correct or not, that would be much appreciated!
The elements of Z/9Z are {0,1,2,3,4,5,6,7,8} with operation modulo9.
The elements (1,2,4,5,7,8} have order 9 and generate the whole group.
{0,3,6} has order 3.
Therefore there are two subgroups.