show that the group of rational numbers under addition can not be written as direct sum of two non trivial subgroups
70688
How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups?
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
131306
Prove that a group of order $2^5 \cdot 7^5$ is not simple
25235
Finite abelian groups - direct sum of cyclic subgroup
80381
Groups with "few" subgroups
85106
Group of order 10 has an element of order 5, without using Cauchy's or Sylow's theorems
52089
Group of $2n$ elements, $n$ odd, is not simple
8746
Groups of order $pq$ without using Sylow theorems
622
Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
51196
A group of order $p^2q^2$ is never simple
98731
Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
98440
Show that any non-negative rational integer may be written as the sum of two squares if it is of the form....
75012
Additive group of rationals has no minimal generating set
41688
An elementary problem in Group Theory: the unique noncyclic group of order 4
80976
Direct Product Of Abelian Group
74452
On a uniqueness proof for solutions of $\ a + x = b\,$ in a group