Intereting Posts

Support of $\operatorname{Hom}(R/I, M)$
Extending the logical-or function to a low degree polynomial over a finite field
Every nonzero element in a finite ring is either a unit or a zero divisor
Convergence of $\sum_{n=1}^{\infty}\frac{1}{n^\alpha}$
Prove that $\lim_{x\to 2}x^2=4$ using $\epsilon-\delta$ definition.
How to show $\kappa^{cf(\kappa)}>\kappa$?
Prime elements in $\mathbb{Z}$
Shortest proof for 'hairy ball' theorem
Proving $AE+AP=PD$ In a Certain Right Triangle
A theorem of symmetric positive definite matrix.
Does $\lfloor \sqrt{p} \rfloor$ generate all natural numbers?
On the number of quadratic residues $\pmod{pq}$ where$p$ and $q$ are odd primes.
Bounded variation and differentiability implies absolute continuity
For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
Why the standard deviation of the sample mean is calculated as $\frac{\sigma}{\sqrt{n}}$?

Let $p$ be a prime, let $n>2$ be an integer, and let $G$ be a nonabelian group of order $p^n$. Prove the center of G cannot have order $p^{n-1}$.

Honestly I have no idea where to start. Perhaps prove this by contradiction?

- How to deal with polynomial quotient rings
- abelian groups: proving $\prod\limits_{g\in G}g=\prod\limits_{g\in G}_{g^2=1}g$
- If $G$ is an infinite group, then the group ring $R(G)$ is not semisimple.
- Diophantine equations solved using algebraic numbers?
- What's an Isomorphism?
- What is the meaning of $1/(D+a)$, where $D$ is the derivative operator?

- Mystified by Rotman's proof of normality of index-2 subgroups
- What is a formal polynomial?
- Is it true that $p\mid $?
- Property of short exact sequences.
- Union of the conjugates of a proper subgroup
- Problem from Armstrong's book, “Groups and Symmetry”
- gcd and order of elements of group
- How to recognize a finitely generated abelian group as a product of cyclic groups.
- Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$
- Subgroups of Symmetric groups isomorphic to dihedral group

$G/Z(G)$ has order $p$; so it must be `______`

? But if $G/Z(G)$ is `______`

then it is trivial.

- Non-linear matrix equation solvable with linear algebra?
- Resource request: history of and interconnections between math and physics
- universal property in quotient topology
- isomorphic ideals and projective dimensions of quotients
- Every planar graph has a vertex of degree at most 5.
- Is there a way to calculate $\displaystyle \sum_{k=0}^{n}\sin({2^kx})$?
- Injective function and ultrafilters
- Why is $\text{Hom}(V,W)$ the same thing as $V^* \otimes W$?
- Does a Fourier transformation on a (pseudo-)Riemannian manifold make sense?
- $f,g$ continuous from $X$ to $Y$. if they are agree on a dense set $A$ of $X$ then they agree on $X$
- Exercise from Serre's “Trees” – prove that a given group is trivial
- Calculate Laurent series for $1/ \sin(z)$
- Why do we restrict the definition of Lebesgue Integrability?
- How to find presentation of a group using GAP?
- Exercise books in analysis