User lhl73

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Let $P$ be a Sylow $p$-subgroup of $G$ and suppose $x\in P$ has order $p$ and $C_G(x)$ has cyclic Sylow $p$-subgroups. Prove $P$ is cyclic.

answered Jun 28, 2021 at 13:55

3 votes

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A zero-divisor whose every localization is zero in a Noetherian ring whose every associated prime is minimal

answered Aug 31, 2021 at 11:33

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Is there any isomorphism between these two local rings?

answered Oct 7, 2021 at 0:50

3 votes

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Alternative definition of sheaf associated to a module?

answered Jun 4, 2021 at 12:13

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Calculating the Galois group of $f = X^4+20$.

answered Jun 15, 2020 at 14:17

3 votes

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$M_x$ is free $\Rightarrow \widetilde{M}$ is locally free at $x$

answered Jun 16, 2020 at 0:21

2 votes

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Understanding the steps in Pugh's proof about the Least Upper Bound Property

answered Jun 13, 2020 at 11:04

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Extension of quasi-coherent sheaves

answered Nov 20, 2020 at 8:27

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Proving a matrix is diagonalizable given eigenvectors and information about characteristic polynomial ranks

answered Jan 20, 2022 at 9:11

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Exercise 1.3 in Harris' Algebraic Geometry

answered Sep 20, 2021 at 23:41

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What must be true for thirteen points to impose independent conditions on quartics?

answered Sep 22, 2023 at 8:20

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A curve that intersects $2x^3y^3-30x^2y^2+11xy^3+2x^3-38x^2y+20xy^2-13y^3+16x^2+94xy+10y^2+301x-668y+662$ with multiplicity $3$ or more

answered Jun 8, 2022 at 7:59

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Prove a group of order $22,000$ with $16$ Sylow-$5$ subgroup has a normal (Sylow) $11$ subgroup.

answered Jun 20, 2022 at 11:17

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I have a question of Prop.1.10 of Hartshorne's Algebraic Geometry

answered Apr 19 at 10:50

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Dimension of intersection of distinct subspaces

answered Jun 14, 2020 at 13:07

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Eigenvalues of a matrix in relation to another matrix

answered Feb 3, 2021 at 16:04

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Dense set containing an orthonormal basis

answered Jun 19, 2020 at 16:23

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Two permutations have different parity when each element in one is a function of an element in the other

answered Jun 19, 2020 at 21:25

1 vote

how to show the following problem on combinatorics

answered Jun 26, 2020 at 19:25

1 vote

If $A^T A v = A A^T v = v$ with $A$ not orthogonal. Must $v$ be an eigenvector?

answered Jul 2, 2020 at 14:44

1 vote

Identifying a measure with a function

answered Jun 8, 2020 at 18:22

1 vote

If $\rho\leq\sigma$, is $\operatorname{rank}(\rho)\leq\operatorname{rank}(\sigma)$?

answered Jun 16, 2020 at 13:13

0 votes

A question to a proof regarding to measurable functions with basic topology

answered Jun 19, 2020 at 13:10

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If $T^m(\alpha)=0,$ with $\alpha \in V$ and $m \in \mathbb{N}$, then $T(\alpha)=0$

answered Jun 7, 2020 at 3:18

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Bounded linear operator of $\ell^{2}(\mathbb{N})$ which is normal but not self-adjoint

answered Jun 13, 2020 at 21:46

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Counting summation of binomial coefficients

answered Aug 28, 2020 at 8:16

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Invertiblity of ST and TS for linear maps

answered Nov 23, 2020 at 15:24

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Difference between support of a section and nonvanishing locus of a section.

answered Mar 15, 2023 at 11:09

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If $X$ is a not a rational curve, then $\dim |P|=0$ for all $P$ in $X$.

answered Mar 27, 2023 at 13:04

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Hartshorne Example II.7.8.6

answered Mar 8 at 9:10

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30 Answers

Let $P$ be a Sylow $p$-subgroup of $G$ and suppose $x\in P$ has order $p$ and $C_G(x)$ has cyclic Sylow $p$-subgroups. Prove $P$ is cyclic.

A zero-divisor whose every localization is zero in a Noetherian ring whose every associated prime is minimal

Is there any isomorphism between these two local rings?

Alternative definition of sheaf associated to a module?

Calculating the Galois group of $f = X^4+20$.

$M_x$ is free $\Rightarrow \widetilde{M}$ is locally free at $x$

Understanding the steps in Pugh's proof about the Least Upper Bound Property

Extension of quasi-coherent sheaves

Proving a matrix is diagonalizable given eigenvectors and information about characteristic polynomial ranks

Exercise 1.3 in Harris' Algebraic Geometry

What must be true for thirteen points to impose independent conditions on quartics?

A curve that intersects $2x^3y^3-30x^2y^2+11xy^3+2x^3-38x^2y+20xy^2-13y^3+16x^2+94xy+10y^2+301x-668y+662$ with multiplicity $3$ or more

Prove a group of order $22,000$ with $16$ Sylow-$5$ subgroup has a normal (Sylow) $11$ subgroup.

I have a question of Prop.1.10 of Hartshorne's Algebraic Geometry

Dimension of intersection of distinct subspaces

Eigenvalues of a matrix in relation to another matrix

Dense set containing an orthonormal basis

Two permutations have different parity when each element in one is a function of an element in the other

how to show the following problem on combinatorics

If $A^T A v = A A^T v = v$ with $A$ not orthogonal. Must $v$ be an eigenvector?

Identifying a measure with a function

If $\rho\leq\sigma$, is $\operatorname{rank}(\rho)\leq\operatorname{rank}(\sigma)$?

A question to a proof regarding to measurable functions with basic topology

If $T^m(\alpha)=0,$ with $\alpha \in V$ and $m \in \mathbb{N}$, then $T(\alpha)=0$

Bounded linear operator of $\ell^{2}(\mathbb{N})$ which is normal but not self-adjoint

Counting summation of binomial coefficients

Invertiblity of ST and TS for linear maps

Difference between support of a section and nonvanishing locus of a section.

If $X$ is a not a rational curve, then $\dim |P|=0$ for all $P$ in $X$.

Hartshorne Example II.7.8.6