Let $G_1$ and $G_2$ be groups, each with two/three/four elements. Is it true that $G_1\cong G_2$?
62277
Cayley tables for two non-isomorphic groups of order 4.
113013
Let $M$ and $N$ be two normal subgroups of $G$. Show that $M \cap N$ is also normal in $G$. Then show that $G/(M \cap N) \cong (G/M) \times (G/N)$
63478
Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
102971
Product of all elements of a finite group with an unique element of order 2
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
91997
Product of two subgroups the whole group?
132280
Let $G$ be a group of order 35. Show that $G \cong Z_{35}$
90845
Is this posible in GR $g_{ab}g^{ab}=1$?
45727
If $G$ contains a normal subgroup $H \cong \mathbb{Z_2}$ such that $G/H$ is infinite cyclic, then $G \cong \mathbb{Z} \times \mathbb{Z_2}$
85129
If $H_1, H_2\leq G$ are such that $H_1\cong H_2$ then $G/H_1\cong G/H_2$?
1577
Order of nontrivial elements is 2 implies Abelian group
52121
Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
46260
Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
151727
If $|G/H|=4$ then $G$ is union of three proper subgroups
75068
subgroups of $\mathbb Z / 2 \mathbb Z \times \mathbb Z / 2 \mathbb Z$
37379
Let $G$ a group with normal subgroups $M,N$ such that $M\cap N=\{e\}$. Show that if $G$ is generated by $M\cup N$ then $G\cong M \times N$.
58654
If $|A| > \frac{|G|}{2} $ then $AA = G $