Direct sum of groups vs product
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
74452
On a uniqueness proof for solutions of $\ a + x = b\,$ in a group
31252
"Efficient version" of Cayley's Theorem in Group Theory
24181
Showing that $G$ is a group under an alternative operation.
24561
$\mathbb S_n$ as semidirect product
79425
Prove the direct product of nonzero complex numbers under multiplication.
147298
How to find all subgroups of a direct product?
109675
Finite sum of eigenspaces (with distinct eigenvalues) is a direct sum
70688
How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups?
93617
Sum of the product of two combinations
26330
Why can we modular reduce arguments of sums and products in modular arithmetic?
25421
Simple or not simple Groups
143069
What are the direct summands in $\mathbb{Z}^n$?
70904
Subgroups of $U(n)$ isomorphic to a direct sum of cyclic groups
98734
Order of a product of elements in a generic group
123595
Representations of Direct Sum of Lie Algebras
99346
Prove a result on transitive group actions.