Intereting Posts

Limits of sequences connected with real and complex exponential
A non-noetherian ring with all localizations noetherian
Find combinations of N sets having no more than one item in common.
Why is that the events (Sum of dice roll=6, first die=4) are dependent, but the events (Sum of dice roll=7, first die =4) are independent?
Does the equation has a non-trivial solution?
Wedge product and cross product – any difference?
About the ways prove that a ring is a UFD.
Functional equation $f(xy)=f(x)+f(y)$ and differentiability
Probability Bayesian network problem
How Do You Actually Do Your Mathematics?
Finding integer solutions to $y^2=x^3+7x+9$ using WolframAlpha
if $abc=1$, then $a^2+b^2+c^2\ge a+b+c$
Let $A , B\subseteq\mathbb{R}$. If $A$ is closed and $B$ is compact, is $A\cdot B$ closed?
Definition of time-constructible function
Smallest closed ball enclosing a compact set

There is a well-known classification of finite abelian groups into products of cyclic groups.

What about finite abelian group schemes, where we may put in the qualifiers “affine”, “etale”, or “connected” if it helps?

There are some easy examples showing that the theory is richer than that of groups:

- A question concerning unipotent matrices and a basis choice
- Geometric difference between two actions of $GL_n(\mathbb{C})$ on $G\times \mathfrak{g}^*$
- Closure of an ideal with respect to p-adic valuation
- Why are parabolic subgroups called “parabolic” subgroups?
- question regarding Waterhouse, affine group schemes
- Orbits of $SL(3, \mathbb{C})/B$

- The constant group scheme $\mathbb{Z}/n\mathbb{Z}$,
- The roots of unity $\mu_n$,
- The group $\alpha_p$ over $k$ of characteristic $p$.

One might hope to obtain more finite abelian group schemes from abelian varieties, but over fields of characteristic $p$, the $p$-torsion of an abelian variety is a product of the finite group schemes already mentioned. We also know that any affine etale finite abelian group scheme becomes constant after base change.

Are there other (fundamentally different) examples of finite abelian group schemes, and is there some sort of classification of them all?

- Every finite group is isomorphic to some Galois group for some finite normal extension of some field.
- How to prove that $A_5$ has no subgroup of order 30?
- Compute this factor group: $\mathbb Z_4\times\mathbb Z_6/\langle (0,2) \rangle$
- The center of a group with order $p^2$ is not trivial
- Let $N$ be a normal subgroup of index $m$ in $G$. Prove that $a^m \in N$ for all $a \in G$.
- Normal subgroups of the symmetric group $S_N$
- Product of all elements in finite group
- Is every finite group of isometries a subgroup of a finite reflection group?
- $|G|=12$ and it is isomorphic to $A_4$?
- If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.

- product distribution of two uniform distribution, what about 3 or more
- Proof of Sobolev Inequality Theroem
- Exponent of $GL(n,q)$.
- A simple inequality for floor function
- A classical problem about limit of continuous function at infinity and its connection with Baire Category Theorem
- Proving that the join of a path-connected space with an arbitrary space is simply-connected
- Showing that $x^n -2$ is irreducible in $\mathbb{Q}$
- What is the equation for a line tangent to a circle from a point outside the circle?
- How many numbers of 6 digits, that can be formed with digits 2,3,9. And also divided by 3?
- How does one get the formula for this bijection from $\mathbb{N}\times\mathbb{N}$ onto $\mathbb{N}$?
- Is the space of smooth functions with the sup norm $\sigma$-compact?
- How can I prove that Game of Life's evolution function is continuous?
- Show that every large integer has a large prime-power factor
- If $G$ is an infinite group, then the group ring $R(G)$ is not semisimple.
- Isomorphism between fields