Bernard Pan's user avatar
Bernard Pan's user avatar
Bernard Pan's user avatar
Bernard Pan
  • Member for 3 years, 8 months
  • Last seen this week
6 votes
1 answer
287 views

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

5 votes
1 answer
91 views

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

5 votes
1 answer
203 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.

5 votes
1 answer
687 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

5 votes
1 answer
116 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 $\frak p_1,q_1$

4 votes
1 answer
131 views

Kronecker Product of Normal Matrices

4 votes
2 answers
145 views

Prove the given matrix is invertible

3 votes
2 answers
178 views

Prove the following matrix commute with every matrix

3 votes
1 answer
181 views

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

3 votes
1 answer
335 views

Determinant of Kronecker Product

3 votes
2 answers
261 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 $\gcd(Ma_1/b_1,\ldots,Ma_n/b_n)=1$.

3 votes
1 answer
111 views

Complement for the Center of a Group

2 votes
1 answer
122 views

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

2 votes
0 answers
25 views

Every Cyclic Submodule of $M$ is Simple $\implies$ $M$ is Simple or the Ring of Homotheties on $M$ is a Division Ring

2 votes
1 answer
168 views

Injectivity and Surjectivity of Induced Map Under Universal Property of Localization

2 votes
1 answer
268 views

Proof of a Topological Embedding

2 votes
2 answers
742 views

Proof of Ascoli's theorem

2 votes
2 answers
113 views

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

2 votes
0 answers
105 views

Compute the rank of an orthgonal projection efficiently

1 vote
1 answer
297 views

Proof Verification: Equivalent Definition for Locally Compact Hausdorff Space

1 vote
1 answer
34 views

Formula about Closure of Sets

1 vote
1 answer
102 views

Why these two topological spaces are not homeomorphic

1 vote
0 answers
40 views

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

1 vote
0 answers
20 views

Inequality of Probability

1 vote
1 answer
140 views

Moore-Penrose Inverse Formula

1 vote
2 answers
84 views

Matrix Determinant Formula

1 vote
1 answer
37 views

Image of Sum of Submodules

1 vote
1 answer
60 views

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

1 vote
1 answer
32 views

Homomorphism from a simple module to a direct sum of itself

0 votes
1 answer
43 views

If an Artinian module $M$ is a sum of submodules of length $\le n$, then it is also of finite length