Hello all I have taken a group theory course where we are now covering p groups and we I have met the following exercise:
Let $ G = Z/(p^n) $ is a(n Abelian) group of order $ p^n $ for a prime $ p $ and a natural $ n $.
We are asked to show G cannot be written as a direct sum of two non trivial proper subgroups
Now, first of all what does $ Z/(p^n) $ mean exactly? I have not met this notation previously.
And finally to prove the result, I have found a link on here with a similar problem where the proposed (and accepted) answer was to assume to get contradiction we could do such a thing but then the two non trivial subgroups would intersect nontrivially and the answer stated that for this group this cannot happen which I do not understand how to show. I certainly appreciate all kind helpers willing to assist a novice, thanks