When can the isomorphism theorem for Groups be rewritten as a direct product?
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
111375
Normality of subgroups and Sylow groups under homomorphisms...
157040
For groups $A,B,C$, if $A\times B$ and $A\times C$ are isomorphic do we have $B$ isomorphic to $C$?
31252
"Efficient version" of Cayley's Theorem in Group Theory
70688
How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups?
129120
Example of a group $G$ such that $G = N_1\cdots N_n$ and $N_i \cap N_j = \{e\}$ for all $i \neq j$ but $G$ is not the internal direct product of them.
36980
Prove the third isomorphism theorem
46260
Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
99538
Non-trivial groups pairwise non-isomorphic with isomorphic direct products
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
24966
Converse of Lagrange's theorem for abelian groups
157915
Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
33294
The correspondence theorem for groups
47617
Are groups with all the same Hom sets already isomorphic?
66863
How is the quotient group related to the direct product group?
18540
Isomorphism from $\mathbb{C}[G]$ to $\prod_{i=1}^h M_{n_i}(\mathbb{C})$.
32428
Group homomorphisms and which of the following statements are true (NBHM-$2014$)