User Student

7

votes

3

answers

111

views

Pointwise convergence of sequence $(f_n)_n$ of functions to $f$ and changing limits

Aug 20 '18 at 21:43 MathIsNice1729 4,302

5

votes

5

answers

153

views

Computing $7^{13} \mod 40$

number-theory elementary-number-theory proof-verification

Feb 17 '17 at 21:12 Steven Alexis Gregory 25.1k

5

votes

2

answers

640

views

Compute $5!25! \mod 31$

number-theory elementary-number-theory proof-verification

Feb 17 '17 at 12:09 Michael Rozenberg 184k

5

votes

1

answer

4k

views

Tensor product of localization is isomorphic to localization of tensor product

commutative-algebra tensor-products

Jan 17 '17 at 7:11 Zelos Malum 6,277

4

votes

1

answer

68

views

Subgroups of finitely generated group are not necessarily finitely generated (proof).

group-theory permutations finitely-generated combinatorial-group-theory

Apr 3 at 7:57 Derek Holt 75.6k

1

4

votes

2

answers

348

views

Restriction of homomorphism to finite index subgroup gives finite index subgroup of kernel

abstract-algebra group-homomorphism

May 1 '18 at 22:54 stewbasic 6,011

4

votes

1

answer

254

views

Boundary $\partial F_n$ of a free group $F_n$

geometric-group-theory automorphism-group

Mar 6 '18 at 11:53 Najib Idrissi 49.8k

4

votes

1

answer

287

views

Prove that the following map has at least $k-2$ fixed points

general-topology group-theory algebraic-topology

Jan 17 '18 at 13:32 sryscad 3

1

4

votes

2

answers

61

views

If $x = y^3$ in $\mathbb{Z} + \frac{-1 + \sqrt{-3}}{2}\mathbb{Z}$, then there is some $w \in \mathbb{Z} + \sqrt{-3}\mathbb{Z}$ such that $x = w^3$.

number-theory ring-theory unique-factorization-domains

May 15 '17 at 13:03 quasi 54.3k

1

4

votes

1

answer

340

views

isomorphic extension fields of the $p$-adic numbers

number-theory extension-field p-adic-number-theory group-homomorphism

May 2 '17 at 17:15 Student 3,857

4

votes

2

answers

417

views

Inverse image of a Noetherian module under a module morphism

abstract-algebra noetherian

Jan 14 '17 at 16:03 Bernard 169k

3

votes

3

answers

154

views

Prove that $\sum_{k = 0}^{49}(-1)^k\binom{99}{2k} = -2^{49}$

binomial-coefficients binomial-theorem

Dec 24 '18 at 18:29 Mike Earnest 51.7k

1

3

votes

2

answers

3k

views

Why is this function only differentiable at zero?

calculus limits derivatives

Aug 28 '18 at 11:09 Nosrati 29.3k

3

votes

1

answer

245

views

$x_n \to x \in \mathbb{R}$ and $y_n \to 0 $. What about $\frac{x_n}{y_n}$?

real-analysis sequences-and-series proof-verification convergence-divergence proof-writing

Jul 15 '18 at 8:55 Jneven 2,613

3

votes

2

answers

82

views

image of homomorphism contains free group, then so does domain

abstract-algebra group-homomorphism free-groups

May 26 '18 at 15:19 Billy 5,044

3

votes

1

answer

118

views

automorphism of free group $F_n$ fixing $F_{n-1}$ and image of $n$th generator

group-theory reference-request free-groups geometric-group-theory automorphism-group

May 9 '18 at 10:21 user1729 27.6k

3

votes

1

answer

106

views

components of subgraph determine subgroups up to conjugacy

graph-theory algebraic-topology free-groups

Mar 20 '18 at 19:20 Dap 24.6k

1

3

votes

2

answers

121

views

Proving that $a+b\sqrt{-3}$ is a cube if $a^2 + 3b^2 = c^3$

abstract-algebra ring-theory factoring unique-factorization-domains

May 18 '17 at 19:23 Student 3,857

1

3

votes

0

answers

72

views

Factoring $a + b\frac{1 + \sqrt{5}}{2}$ if $a^2 + ab - b^2 = a+b$

number-theory ring-theory factoring unique-factorization-domains

May 16 '17 at 14:47 Student 3,857

1

3

votes

0

answers

134

views

showing elements in $\mathbb{Z}+\frac{1 + \sqrt{5}}{2}\mathbb{Z}$ are associated

number-theory ring-theory factoring unique-factorization-domains

May 16 '17 at 12:45 Student 3,857

1

3

votes

3

answers

128

views

Question about definition of graded ring

abstract-algebra graded-rings

Apr 3 '17 at 12:21 CommunityBot 1

3

votes

2

answers

664

views

Proving $(x_1 - a_1, \ldots, x_n -a_n)$ is a maximal ideal [duplicate]

abstract-algebra ring-homomorphism

Apr 1 '17 at 11:46 CommunityBot 1

3

votes

1

answer

319

views

Proof about positive semi-definite matrix

linear-algebra proof-verification norm positive-definite

Mar 16 '17 at 10:54 CommunityBot 1

3

votes

3

answers

71

views

Find all couples $(a,b) \in \mathbb{Z}^2$

number-theory elementary-number-theory

Feb 14 '17 at 15:54 CommunityBot 1

3

votes

4

answers

3k

views

Number of elements of order 2

group-theory finite-groups

Feb 12 '17 at 8:15 pepa.dvorak 959

2

votes

2

answers

147

views

finding smallest natural number $n$ such that $n \equiv 1023 \bmod 2015$ and $n \equiv 1302 \bmod 2016$

number-theory elementary-number-theory

Apr 19 at 19:23 Bill Dubuque 253k

2

votes

2

answers

98

views

Let K be a non-abelian subgroup of dihedral group and $H = K \cap \{1, a, a^2, \ldots, a^{n-1}\}$ then the index of H in K is 2.

group-theory finite-groups dihedral-groups

Jul 26 '19 at 16:14 Marc Bogaerts 5,868

2

votes

1

answer

33

views

combinatorics problem: ordering people from small to large. Is my solution correct?

combinatorics proof-verification alternative-proof

Apr 7 '19 at 16:08 N. F. Taussig 62.7k

2

votes

2

answers

172

views

lim inf and lim sup of sequence obtained from combination of two sequences

real-analysis sequences-and-series convergence-divergence limsup-and-liminf

Jul 15 '18 at 10:37 mechanodroid 43k

2

votes

1

answer

174

views

Collapsing subgraph: Bogopolski's "Introduction to group theory"

graph-theory proof-explanation

Feb 16 '18 at 18:04 BallBoy 14.1k

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82 Questions

Pointwise convergence of sequence $(f_n)_n$ of functions to $f$ and changing limits

Computing $7^{13} \mod 40$

Compute $5!25! \mod 31$

Tensor product of localization is isomorphic to localization of tensor product

Subgroups of finitely generated group are not necessarily finitely generated (proof).

Restriction of homomorphism to finite index subgroup gives finite index subgroup of kernel

Boundary $\partial F_n$ of a free group $F_n$

Prove that the following map has at least $k-2$ fixed points

If $x = y^3$ in $\mathbb{Z} + \frac{-1 + \sqrt{-3}}{2}\mathbb{Z}$, then there is some $w \in \mathbb{Z} + \sqrt{-3}\mathbb{Z}$ such that $x = w^3$.

isomorphic extension fields of the $p$-adic numbers

Inverse image of a Noetherian module under a module morphism

Prove that $\sum_{k = 0}^{49}(-1)^k\binom{99}{2k} = -2^{49}$

Why is this function only differentiable at zero?

$x_n \to x \in \mathbb{R}$ and $y_n \to 0 $. What about $\frac{x_n}{y_n}$?

image of homomorphism contains free group, then so does domain

automorphism of free group $F_n$ fixing $F_{n-1}$ and image of $n$th generator

components of subgraph determine subgroups up to conjugacy

Proving that $a+b\sqrt{-3}$ is a cube if $a^2 + 3b^2 = c^3$

Factoring $a + b\frac{1 + \sqrt{5}}{2}$ if $a^2 + ab - b^2 = a+b$

showing elements in $\mathbb{Z}+\frac{1 + \sqrt{5}}{2}\mathbb{Z}$ are associated

Question about definition of graded ring

Proving $(x_1 - a_1, \ldots, x_n -a_n)$ is a maximal ideal [duplicate]

Proof about positive semi-definite matrix

Find all couples $(a,b) \in \mathbb{Z}^2$

Number of elements of order 2

finding smallest natural number $n$ such that $n \equiv 1023 \bmod 2015$ and $n \equiv 1302 \bmod 2016$

Let K be a non-abelian subgroup of dihedral group and $H = K \cap \{1, a, a^2, \ldots, a^{n-1}\}$ then the index of H in K is 2.

combinatorics problem: ordering people from small to large. Is my solution correct?

lim inf and lim sup of sequence obtained from combination of two sequences

Collapsing subgraph: Bogopolski's "Introduction to group theory"