User Dietrich Burde

75 votes

Accepted

If I know the order of every element in a group, do I know the group?

answered May 24, 2015 at 16:22

41 votes

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Complete classification of the groups for which converse of Lagrange's Theorem holds

abstract-algebra group-theory reference-request finite-groups

answered Feb 14, 2017 at 14:48

38 votes

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Normal subgroups of dihedral groups

group-theory finite-groups

answered Sep 5, 2013 at 12:13

38 votes

Let $A=(a_{ij})$ be an $n\times n$ matrix. Suppose that $A^2$ is diagonal. Must $A$ be diagonal?

linear-algebra matrices matrix-decomposition

answered Apr 12, 2018 at 11:28

37 votes

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Do commuting matrices share the same eigenvectors?

linear-algebra matrices eigenvalues-eigenvectors

answered Apr 9, 2015 at 14:47

35 votes

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Prime numbers the rank of which is also a prime.

sequences-and-series prime-numbers distribution-of-primes

answered Aug 24, 2017 at 13:20

30 votes

If the field of a vector space weren't characteristic zero, then what would change in the theory?

linear-algebra matrices vector-spaces field-theory linear-transformations

answered Jun 30, 2017 at 14:22

25 votes

All Sylow $p$-subgroups of $GL_2(\mathbb F_p)$?

abstract-algebra group-theory finite-groups sylow-theory

answered Nov 17, 2016 at 19:54

23 votes

What is the correct spelling of Paul Erdős's name?

reference-request soft-question

answered Oct 6, 2013 at 19:01

23 votes

Computing the Galois group of polynomials $x^n-a \in \mathbb{Q}[x]$

galois-theory

answered Dec 23, 2016 at 14:56

23 votes

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Book recomendation for Elliptic-curve cryptography

abstract-algebra book-recommendation elliptic-curves cryptography

answered Dec 19, 2017 at 17:32

22 votes

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Show how to calculate the Riemann zeta function for the first non-trivial zero

complex-numbers riemann-zeta

answered Sep 11, 2013 at 7:48

20 votes

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Would proof of Legendre's conjecture also prove Riemann's hypothesis?

number-theory elementary-number-theory prime-numbers analytic-number-theory riemann-hypothesis

answered Sep 3, 2013 at 8:45

20 votes

Find some digits of $17!$

elementary-number-theory factorial

answered Feb 28, 2019 at 19:12

20 votes

Simple theorems that are instances of deep mathematics

soft-question big-list

answered Apr 4, 2017 at 18:35

19 votes

Accepted

Finite groups as subgroups of dihedral groups

abstract-algebra group-theory finite-groups

answered Sep 9, 2016 at 18:07

18 votes

I need to determine the subgroups of the dihedral group of order 8, $D_4$.

group-theory dihedral-groups

answered Sep 16, 2016 at 15:31

17 votes

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Is there any perfect squares that are also binomial coefficients?

combinatorics number-theory

answered May 2, 2014 at 12:07

17 votes

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How do I make this simple proof better (and more correct?)

proof-writing

answered Sep 28, 2014 at 15:41

16 votes

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$ABAB=0_{n\times n}$, then must $BABA$ be $0_{n\times n}$?

linear-algebra matrices nilpotence

answered Jan 5, 2014 at 16:49

16 votes

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Largest multiple of $7$ lower than some $78$-digit number?

elementary-number-theory modular-arithmetic arithmetic

answered Mar 18, 2019 at 9:33

16 votes

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What is the intuition behind simple Lie groups?

representation-theory lie-groups lie-algebras simple-groups

answered May 8 at 12:02

15 votes

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Why Zariski topology is not Hausdorff

real-analysis algebraic-geometry

answered Dec 17, 2014 at 10:00

15 votes

Why is $ (2+\sqrt{3})^n+(2-\sqrt{3})^n$ an integer?

algebra-precalculus elementary-number-theory

answered Aug 25, 2016 at 10:19

15 votes

Accepted

How to find a Cartan subalgebra of $so(3)$.

lie-algebras

answered Jul 7, 2016 at 9:20

14 votes

When is the Killing form null?

lie-algebras

answered Dec 18, 2013 at 15:46

14 votes

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Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID

number-theory algebraic-number-theory principal-ideal-domains

answered Oct 30, 2014 at 19:19

14 votes

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Conjecture: All but 21 non-square integers are the sum of a square and a prime

number-theory prime-numbers asymptotics sums-of-squares goldbachs-conjecture

answered Jun 7, 2020 at 19:01

13 votes

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Why are the rational numbers not continuous?

real-analysis rational-numbers

answered Feb 11, 2014 at 9:44

13 votes

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Minimize the product of two positive integers $a,b$ that satisfy $2013+ a^2 = b^2$

elementary-number-theory

answered Oct 13, 2014 at 15:16

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4,294 Answers

If I know the order of every element in a group, do I know the group?

Complete classification of the groups for which converse of Lagrange's Theorem holds

Normal subgroups of dihedral groups

Let $A=(a_{ij})$ be an $n\times n$ matrix. Suppose that $A^2$ is diagonal. Must $A$ be diagonal?

Do commuting matrices share the same eigenvectors?

Prime numbers the rank of which is also a prime.

If the field of a vector space weren't characteristic zero, then what would change in the theory?

All Sylow $p$-subgroups of $GL_2(\mathbb F_p)$?

What is the correct spelling of Paul Erdős's name?

Computing the Galois group of polynomials $x^n-a \in \mathbb{Q}[x]$

Book recomendation for Elliptic-curve cryptography

Show how to calculate the Riemann zeta function for the first non-trivial zero

Would proof of Legendre's conjecture also prove Riemann's hypothesis?

Find some digits of $17!$

Simple theorems that are instances of deep mathematics

Finite groups as subgroups of dihedral groups

I need to determine the subgroups of the dihedral group of order 8, $D_4$.

Is there any perfect squares that are also binomial coefficients?

How do I make this simple proof better (and more correct?)

$ABAB=0_{n\times n}$, then must $BABA$ be $0_{n\times n}$?

Largest multiple of $7$ lower than some $78$-digit number?

What is the intuition behind simple Lie groups?

Why Zariski topology is not Hausdorff

Why is $ (2+\sqrt{3})^n+(2-\sqrt{3})^n$ an integer?

How to find a Cartan subalgebra of $so(3)$.

When is the Killing form null?

Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID

Conjecture: All but 21 non-square integers are the sum of a square and a prime

Why are the rational numbers not continuous?

Minimize the product of two positive integers $a,b$ that satisfy $2013+ a^2 = b^2$