User Bernard Pan

6 votes

1 answer

230 views

Find an element of order $p$ in a non-abelian group $G$ of order $p^3$ where $p$ is an odd prime

asked Aug 9, 2021 at 18:52

5 votes

1 answer

87 views

Uniqueness of Semidirect Product $(\mathbb{F}_p\times\mathbb{F}_p)\rtimes\mathbb{F}_p$

asked Aug 10, 2021 at 2:12

5 votes

1 answer

194 views

Let $G$ be a group with center $Z<G$. Prove that if every element in $G\setminus Z$ has finite order, then $G$ is periodic.

asked Jan 9, 2021 at 23:15

5 votes

1 answer

111 views

Prime $\frak p\subset q\implies\exists$ prime $\frak p_1,q_1:p\subseteq p_1\subset q_1\subseteq q$ with no prime ideals between $\frak p_1,q_1$

asked Feb 22 at 22:08

4 votes

1 answer

116 views

Kronecker Product of Normal Matrices

asked Mar 22, 2022 at 4:07

4 votes

1 answer

587 views

If the Riemann-Stieltjes integral $\int_a^b{f\,dg}$ exists for every $f\in\mathcal{R}[a,b]$, then $g$ is absolutely continuous

asked Nov 24, 2022 at 4:09

4 votes

2 answers

142 views

Prove the given matrix is invertible

asked Mar 17, 2022 at 23:52

3 votes

2 answers

168 views

Prove the following matrix commute with every matrix

asked Jan 31, 2022 at 7:42

3 votes

1 answer

166 views

Define a norm on $\mathbb{R}^3$ such that unit vectors have norm $1$ while $\|(1,1,1)\|<\frac{1}{100}$

asked Apr 28, 2021 at 0:42

3 votes

1 answer

320 views

Determinant of Kronecker Product

asked Nov 19, 2020 at 22:46

3 votes

2 answers

253 views

Let $a_1/b_1,\ldots,a_n/b_n$ be rational numbers in lowest terms. If $M={\rm lcm}(b_1,\ldots,b_n)$, prove $\gcd(Ma_1/b_1,\ldots,Ma_n/b_n)=1$.

asked Dec 8, 2020 at 2:23

3 votes

1 answer

100 views

Complement for the Center of a Group

asked Sep 10 at 18:19

2 votes

1 answer

110 views

Proof of $\operatorname{Aut}_G(G/H)\cong N_G(H)/H$

asked Sep 24 at 4:22

2 votes

1 answer

140 views

Injectivity and Surjectivity of Induced Map Under Universal Property of Localization

asked Mar 5 at 5:48

2 votes

1 answer

248 views

Proof of a Topological Embedding

asked Jun 29, 2020 at 2:19

2 votes

2 answers

696 views

Proof of Ascoli's theorem

asked Jun 30, 2020 at 15:32

2 votes

2 answers

107 views

Question about proof on left module structure of $M\otimes N$

asked Jul 10, 2021 at 20:42

2 votes

0 answers

99 views

Compute the rank of an orthgonal projection efficiently

asked Mar 19, 2022 at 4:54

1 vote

1 answer

270 views

Proof Verification: Equivalent Definition for Locally Compact Hausdorff Space

asked Jun 17, 2020 at 20:19

1 vote

1 answer

32 views

Formula about Closure of Sets

asked Jun 18, 2020 at 14:43

1 vote

1 answer

101 views

Why these two topological spaces are not homeomorphic

asked Jun 19, 2020 at 18:26

1 vote

0 answers

39 views

Proof Verification: $h(x)$ is a power of $p(x)$

asked Dec 13, 2020 at 18:17

1 vote

0 answers

20 views

Inequality of Probability

asked Nov 12, 2020 at 16:58

1 vote

1 answer

134 views

Moore-Penrose Inverse Formula

asked Nov 15, 2020 at 22:01

1 vote

2 answers

83 views

Matrix Determinant Formula

asked Nov 18, 2020 at 18:22

1 vote

1 answer

57 views

Construct Two Lebesgue Integrable Functions whose Product is not Lebesgue Integrable for Arbitrary $|E|>0$

asked Oct 25, 2022 at 3:17

0 votes

1 answer

41 views

Inequalities on positive semi-definite matrices

asked May 16, 2022 at 20:57

0 votes

2 answers

116 views

Initial Function in the Iterative Construction of the Cantor-Lebesgue Staircase Function

asked Oct 15, 2022 at 1:29

0 votes

1 answer

218 views

Diagonal Sub-Matrix of A Positive Definite Matrix

asked Nov 11, 2020 at 17:17

0 votes

0 answers

33 views

Standard/Wildly-Accepted Terminology for This Concept

asked Jul 13, 2021 at 17:35

Stack Exchange Network

30 Questions

Find an element of order $p$ in a non-abelian group $G$ of order $p^3$ where $p$ is an odd prime

Uniqueness of Semidirect Product $(\mathbb{F}_p\times\mathbb{F}_p)\rtimes\mathbb{F}_p$

Let $G$ be a group with center $Z<G$. Prove that if every element in $G\setminus Z$ has finite order, then $G$ is periodic.

Prime $\frak p\subset q\implies\exists$ prime $\frak p_1,q_1:p\subseteq p_1\subset q_1\subseteq q$ with no prime ideals between $\frak p_1,q_1$

Kronecker Product of Normal Matrices

If the Riemann-Stieltjes integral $\int_a^b{f\,dg}$ exists for every $f\in\mathcal{R}[a,b]$, then $g$ is absolutely continuous

Prove the given matrix is invertible

Prove the following matrix commute with every matrix

Define a norm on $\mathbb{R}^3$ such that unit vectors have norm $1$ while $\|(1,1,1)\|<\frac{1}{100}$

Determinant of Kronecker Product

Let $a_1/b_1,\ldots,a_n/b_n$ be rational numbers in lowest terms. If $M={\rm lcm}(b_1,\ldots,b_n)$, prove $\gcd(Ma_1/b_1,\ldots,Ma_n/b_n)=1$.

Complement for the Center of a Group

Proof of $\operatorname{Aut}_G(G/H)\cong N_G(H)/H$

Injectivity and Surjectivity of Induced Map Under Universal Property of Localization

Proof of a Topological Embedding

Proof of Ascoli's theorem

Question about proof on left module structure of $M\otimes N$

Compute the rank of an orthgonal projection efficiently

Proof Verification: Equivalent Definition for Locally Compact Hausdorff Space

Formula about Closure of Sets

Why these two topological spaces are not homeomorphic

Proof Verification: $h(x)$ is a power of $p(x)$

Inequality of Probability

Moore-Penrose Inverse Formula

Matrix Determinant Formula

Construct Two Lebesgue Integrable Functions whose Product is not Lebesgue Integrable for Arbitrary $|E|>0$

Inequalities on positive semi-definite matrices

Initial Function in the Iterative Construction of the Cantor-Lebesgue Staircase Function

Diagonal Sub-Matrix of A Positive Definite Matrix

Standard/Wildly-Accepted Terminology for This Concept