or Order of nontrivial elements is 2 implies Abelian groupīut for the case of 4 elements, we can also find this group by filling We know that every group with this property is commutative, see Prove that if $g^2=e$ for all g in G then G is Abelian. So the only remaining case is that there might be a group with four elements where all non-identity elements are of order two. If there is an element of order 4, this group is cyclic. So all other elements must have orders 2 or 4. ![]() ![]() Moreover, only identity has order equal to 1. So possible orders of elements of our are 1, 2, 4. We know that order of any element of a group divides the order of the group.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |