How to compute $\operatorname{Ker}(\phi )$ and $(\phi )(25)$ for $(\phi ):Z\rightarrow Z_{7}$ such that $\phi(1)=4$?
97258
Give $\ker(\phi)$ for $\phi: \mathbb{Z} \to \mathbb{Z_7}$ such that $\phi(1)=4$
62076
Can any channel be written as $\Phi(X)=\operatorname{Tr}_{\mathcal Z}[U(X\otimes \sigma)U^\dagger]$ for any state $\sigma$?
34714
What is the relationship between $\ker(A), \ker(A^2), \ldots, \ker(A^n)$?
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
55621
Show that if $c_1, c_2, \ldots, c_{\phi(m)}$ is a reduced residue system modulo m, $m \neq 2$ then $c_1 + \cdots+ c_{\phi(m)} \equiv 0 \pmod{m}$
9753
How to solve the equation $\phi(n) = k$?
122312
How can I compute $\mathrm{Aut}(\mathbb{Z}/4\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z})$?
90433
Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$
74187
$\operatorname{ord}(u)=r,\,\operatorname{ord}(v)=s$ $\,\Rightarrow\,\operatorname{ord}(uv)=rs\,$ if $\,r,s\,$ (co)primes
34960
Lower bound for $\phi(n)$: Is $n/5  1$?
9140
Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
23037
Computing the order of $\mathrm{SL}_2(\mathbb F_p)$ as the kernel of $\mathrm{GL}_2(\mathbb F_p)$
45998
The range of $T^*$ is the orthogonal complement of $\ker(T)$
63803
Calculating the tensor product $\mathbb{Z}/n\mathbb{Z} \otimes_{\mathbb Z} \mathbb{Z}/n\mathbb{Z}$
136623
Hints/ Solution in finding a formula $\phi(n)$ for a binary square matrix
104982
Determine $\phi(2^{399}+1)$