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awarded  Constituent
Dec
19
revised If $G/G'$ is finite, then $|Z(G)| < \infty$
Improves formatting
Dec
19
suggested approved edit on If $G/G'$ is finite, then $|Z(G)| < \infty$
Dec
15
awarded  Caucus
Dec
15
awarded  Critic
Dec
15
comment $a_1^3+a_2^3+…+a_n^3=0 \Rightarrow a_1+a_2+…+a_n=0$ it is true or not?
Please reconsider whether this should be tagged abstract-algebra. The tag description says: “Abstract algebra is the study of algebraic objects. Some of the more common algebraic objects are groups, rings, fields, vector spaces, modules, and other advanced topics.”
Dec
15
comment Is there any solution to this problem?
Please put a bit of effort into writing your question. Show what you have tried, and where you are stuck. Also, please do not abuse that tag number-theory. If you do not know what a tag means, don't use it. From the tag description: “Questions on more advanced topics of number theory. Consider first if (elementary-number-theory) might be a more appropriate tag before adding this tag.” Hint: elementary-number-theory is not more appropriate.
Sep
30
awarded  Explainer
Jun
16
comment Irreducibility of $x^n-x-1$ over $\mathbb Q$
@Corvus — To echo TedShifrin, the polynomial ring $\mathbb{F}_{p}[X]$ is infinite, the set $\mathrm{Map}(\mathbb{F}_{p}, \mathbb{F}_{p})$ is finite. Hence the natural map $\mathbb{F}_{p}[X] \to \mathrm{Map}(\mathbb{F}_{p}, \mathbb{F}_{p})$ is not injective. To stress the difference, let me ‘prove’ that $\mathbb{F}_{2}$ is algebraically closed: Take a non-constant polynomial $f$, then $f$ is not constant $1$, and as $\mathbb{F}_{2}$ has only two elements, $f(x) = 0$ for some $x \in \mathbb{F}_{2}$. Thus $f$ has a zero, hence $\mathbb{F}_{2}$ is algebraically closed. $\square$ Spot the error.
Jun
3
comment When do we have that Absolute hodge classes= Hodge classes for complex projective manifolds?
I think, if the Lefschetz operators are algebraic, then André's motivated cycles are algebraic.
May
27
comment A simpler expression that is always smaller or larger
Well, write your function as $an^2 + bn + c$, where $a,b,c$ are fractions. Then it is already pretty simple. Next, you can consider if you want your estimate on a particular domain, or on all of $\mathbb{R}$. Depending on the answer, you might be able to round $a$ to an integer, and get rid of $b$ and $c$.
May
27
answered A simpler expression that is always smaller or larger
May
27
answered Why do the addition of linear equations all pass through the same point
May
27
suggested rejected edit on can someone give me the solution with the proof?
May
27
comment Dimensions of eigenspaces.
Figure out what it means to be in either of the eigenspaces: How are matrices $A$ called that satisfy $A = A^{\perp}$, and what if $A = -A^{\perp}$? It shouldn't be too hard to figure out a basis/the dimension for the eigenspaces, once you have done that.
May
26
comment What topological restrictions are there for a topological space to be a group?
I don't think your statement is correct. For example $\mathbb{C}$ is non-compact, a Riemann-surface, and carries a group structure. Probably the statement you mean is: If $X$ (your Riemann surface) is compact, then it admits a group structure if and only if the genus is $1$.
May
12
answered Equivalence between exact sequence of module and its induced one.
May
12
comment Equivalence between exact sequence of module and its induced one.
I think you need to add “for all $Y$” after the exact sequence of $\mathrm{Hom}$-sets. Otherwise, take $Y = 0$; then the sequence of $\mathrm{Hom}$-sets is exact, independent of what $X$, $X'$, and $X''$ are.
May
12
answered Singular points query
May
10
comment Positive and negative complex numbers?
In other words: squares are positive, and everything is a square.