Show that $H$ is a group, and that it is isomorphic to $G$
158490
Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
87766
Using Cayley's Theorem to find an isomorphic subgroup.
130081
Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.
15276
$G \times H \cong G \times K$ , then $ K \cong H$
157145
Subgroup of $S_8$ isomorphic to $G$
148881
Aut(GxH) isomorphic to Aut(G)xAut(H)
58707
Prove Quotient Group Isomorphism
24181
Showing that $G$ is a group under an alternative operation.
56650
Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
108213
$N_1,N_2,N_3 \unlhd G, N_i\cap N_j =\{e\}, G = N_iN_j$. Want to show that $G$ is abelian, $N_i$ are isomorphic.
11957
G is the product of its Sylow subgroups
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
79452
How to prove that it is a group?
152603
Group isomorphic to its automorphism group
27728
Question on a homomorphism of a set G.