I have a problem. suppose H,K are subgroups, and HK= (hk, h in H, k in K), KH=(kh, h in H, k in K). I need to show that KH is a group iff HK=KH. can you help me fo the forward proof?
G has exactly 8 elements of order 10. i need to find the number of cyclic subgroups of order 10. for each of the elements of order 10, say, a, |<a>|=|a|=10. so there are 8 cyclic subgroups of order 10
suppose that G has exactly 8 elements of order then. how many cyclic subgroups of order 10 does G have? i guess for all a, |<a>|=8, so, i have found 8 cyclic subgroups of order 10. are there others?