Intereting Posts

Least Square fit for signal data (360 points)
Showing the set $A+B$ is closed.
Prove that distinct Fermat Numbers are relatively prime
Prove that $\lim\limits_{x\to\infty} \frac{\Gamma(x+1,x(1+\epsilon))}{x\Gamma(x)}=0$.
How to show the inequality is strict?
Two Limits Equal – Proof that $\lim_{n\to\infty }a_n=L$ implies $\lim_{n\to\infty }\frac{\sum_1^na_k}n=L$
Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
Find the approximate center of a circle passing through more than three points
Constructing a certain rational number (Rudin)
gradient descent optimal step size
Condition for $a, b + \omega$ to be the canonical basis of an ideal of a quadratic order
Can sum of a rational number and its reciprocal be an integer?
Deriving Fourier inversion formula from Fourier series
Mathematical questions whose answer depends on the Axiom of Choice
How to apply Stokes' Theorem for manifolds with boundary

Prove that there is no homomorphism from $\mathbb{Z}_{8} \oplus \mathbb{Z}_{2}$ ont0 $\mathbb{Z}_{4} \oplus \mathbb{Z}_{4}$.

My idea for the proof : Let $\phi$ be such homomorphism. Since Ker $\phi$ is a subgroup of $\mathbb{Z}_{8} \oplus \mathbb{Z}_{2}$ , then i must find all possible subgroups of it and then prove that $(\mathbb{Z}_{8} \oplus \mathbb{Z}_{2})/$Ker$\:\phi $ is not isomorphic with $\mathbb{Z}_{4} \oplus \mathbb{Z}_{4}$ where Ker $\phi$ can be any of the subgroup. To prove it isnt isomorphic is by finding elements in $\mathbb{Z}_{8} \oplus \mathbb{Z}_{2}$ that has order such that no elements in $\mathbb{Z}_{4} \oplus \mathbb{Z}_{4}$ have that order.

Is there any better way..?

- Algebraic closure for $\mathbb{Q}$ or $\mathbb{F}_p$ without Choice?
- $\mathbb{Q}(\sqrt{2+\sqrt{2}})$ is Galois over $\mathbb{Q}$?
- $gHg^{-1}\subset H$ whenever $Ha\not = Hb$ implies $aH\not =bH$
- All tree orders are lattice orders?
- Vandermonde identity in a ring
- Does $g = x^m - 1 \mid x^{mk} - 1$ for any $k \in \mathbb{N}$?

- Ideals in $\mathbb{Z}$ with three generators (and not with two)
- Question on computing direct limits
- $\mathbb{Q}(\sqrt{2+\sqrt{2}})$ is Galois over $\mathbb{Q}$?
- Odd/Even Permutations
- Projective module over a PID is free?
- Finding all reals such that two field extensions are equal.
- Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
- Mutual set of representatives for left and right cosets: what about infinite groups?
- If $G$ acts transitively and $\Gamma \subseteq \Omega$ is not a block, then each pair of points could be separated
- No simple group of order $96$

A surjective function between two finite sets of the same cardinality is also injective, so your homomorphism would be an isomorphism. This is not possible, because the first group has an element of order $8$ and the second one doesn’t.

- What is the way to see $(S^1\times S^1)/(S^1\vee S^1)\simeq S^2$?
- Inequality understanding
- How do I prove that $\int_0^1 \int_0^1 {{2+x^2-y^2}\over {2-x^2-y^2}} \, dx \, dy=2G?$
- How do we show that $\int_{0}^{1}{\arctan(x\sqrt{x^2+2})\over \sqrt{x^2+2}}\cdot{dx\over x^2+1}=\left({\pi\over 6}\right)^2$
- If the expectation $\langle v,Mv \rangle$ of an operator is $0$ for all $v$ is the operator $0$?
- Counting necklaces with a fixed number of each bead
- Let $G$ be a Lie group. Show that there is a diffeomorphism $TG \cong G \times T_e G$.
- Bounds on $f(k ;a,b) =\frac{ \int_0^\infty \cos(a x) e^{-x^k} \, dx}{ \int_0^\infty \cos(b x) e^{-x^k}\, dx}$
- Prove that $\cot^2{(\pi/7)} + \cot^2{(2\pi/7)} + \cot^2{(3\pi/7)} = 5$
- Turning higher spheres inside out
- Limits and exponents and e exponent form
- Minpoly and Charpoly of block diagonal matrix
- Solving a recurrence of polynomials
- Fundamental group of the torus
- If A is a subset of B, then the closure of A is contained in the closure of B.