Example of Group that is not Internal direct product under weaker condition
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.
131306
Prove that a group of order $2^5 \cdot 7^5$ is not simple
49162
Classify all groups with order $pq$, $p$ is not equal to $q$
8746
Groups of order $pq$ without using Sylow theorems
32127
Example where $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective
119545
Nonzero rationals under multiplication are not a cyclic group
36709
subgroup of direct product of two groups
31392
Examples and Counterexamples of Relations which Satisfy Certain Properties
18003
Standard example where Jacobson radical not equal nilradical
58688
Example of a group where $o(a)$ and $o(b)$ are finite but $o(ab)$ is infinite
123860
When are two direct products of groups isomorphic?
115574
Finitely presented group with fewer relations than generators.
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
146278
Automorphism group of direct product of groups
23077
Prove that the dihedral group $D_4$ can not be written as a direct product of two groups
51196
A group of order $p^2q^2$ is never simple
40743
When a semigroup can be embedded into a group