Congruence on semigroup
39731
The relation $a\theta_n^Sb$ iff $(\forall x\in S^n)\, xa=xb$.
108035
solving diophantine equations using congruences
35124
Can every non-simple group $G$ be written as a semidirect product?
152191
Why is a monoid with right identity and left inverse not necessarily a group?
157806
Order of a element on a Symmetric Group
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
45882
Solving a congruence without Fermat's little theorem
24561
$\mathbb S_n$ as semidirect product
148569
Embeddings $A → B → A$, but $A \not\cong B$?
99346
Prove a result on transitive group actions.
20571
In a monoid, does $x \cdot y=e$ imply $y \cdot x=e$?
131941
Solve quadratic congruences.
49166
$R^n \cong R^m$ iff $n=m$
55902
Show $R[x]/(x)\cong R$
43645
Show that $G/H\cong S_3$
41673
Solve congruence system $\ x\equiv m_i-1 \pmod{m_i}\,$ for $\,i = 1,\ldots, k$
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$