Question

Can there be a different proof for: "If $N$ is a subgroup of a group $G$ of index $2$, then $N$ is a normal subgroup of $G$"?

score 100 · Answer 1 · 2026-04-14 20:10:07

100

Views

Can there be a different proof for: "If $N$ is a subgroup of a group $G$ of index $2$, then $N$ is a normal subgroup of $G$"?

Published on 14 Apr 2026 - 20:10

score 274 · Answer 2 · 2026-04-17 05:03:56

274

Views

If $(a_n)$ is convergent, then $\liminf (a_n+b_n) = \lim a_n + \liminf b_n$

Published on 17 Apr 2026 - 5:03

score 181 · Answer 3 · 2026-04-11 13:18:44

181

Views

Exercise 11, Section 3.5 of Hoffman’s Linear Algebra

Published on 11 Apr 2026 - 13:18

score 211 · Answer 4 · 2026-04-13 18:24:04

211

Views

Can we solve $\frac{dx}{dt} = 3x+3t$ by "multiplying by $dt$"?

Published on 13 Apr 2026 - 18:24

score 186 · Answer 5 · 2026-04-14 12:55:11

186

Views

eigenvalue and inversable matrix-exam problem

Published on 14 Apr 2026 - 12:55

score 144 · Answer 6 · 2026-04-11 07:16:18

144

Views

Easier version of Burnside's transfer theorem

Published on 11 Apr 2026 - 7:16

score 47 · Answer 7 · 2026-04-12 16:09:22

47

Views

(Galois theory )Let $\mathbb F$ be a finite Galois extension of $\mathbb K$...

Published on 12 Apr 2026 - 16:09

score 324 · Answer 8 · 2026-04-28 09:56:33

324

Views

Show that $f(x) = x^5 – 10x + 2 \in \mathbb Q[x]$ is not solvable by radicals.

Published on 28 Apr 2026 - 9:56

score 471 · Answer 9 · 2026-04-15 11:09:13

471

Views

An irreducible polynomial is inseparable iff the exponent of each irreducible factor over an algebraic closure is a multiple of the characteristic

Published on 15 Apr 2026 - 11:09

score 94 · Answer 10 · 2026-04-17 03:29:23

94

Views

A shorter proof of an important lemma: If $\tau$ is an transposition in $\mathscr{S}_n$ and $\phi \in \mathscr{S}_n$ then $ N(\tau\phi)=N(\phi)\pm 1$

Published on 17 Apr 2026 - 3:29

score 81 · Answer 11 · 2026-04-11 17:49:03

81

Views

Why does Equal Finite Disjoint Union of Cartesian Product have Common Refinement?

Published on 11 Apr 2026 - 17:49

score 105 · Answer 12 · 2026-04-12 03:21:19

105

Views

Which One of the Integral Expression is Always Larger?

Published on 12 Apr 2026 - 3:21

score 40 · Answer 13 · 2026-04-10 23:20:36

40

Views

Bounded Integral Sequence is Convergent?

Published on 10 Apr 2026 - 23:20

score 68 · Answer 14 · 2026-04-13 08:30:07

68

Views

Limit in Total Variation Converging to Zero Implies Absolute Continuity?

Published on 13 Apr 2026 - 8:30

score 87 · Answer 15 · 2026-04-11 16:04:04

87

Views

Convergence in Integral and Bounded in Lp Implies Convergence in Measure?

Published on 11 Apr 2026 - 16:04

List Question

Can there be a different proof for: "If $N$ is a subgroup of a group $G$ of index $2$, then $N$ is a normal subgroup of $G$"?

If $(a_n)$ is convergent, then $\liminf (a_n+b_n) = \lim a_n + \liminf b_n$

Exercise 11, Section 3.5 of Hoffman’s Linear Algebra

Can we solve $\frac{dx}{dt} = 3x+3t$ by "multiplying by $dt$"?

eigenvalue and inversable matrix-exam problem

Easier version of Burnside's transfer theorem

(Galois theory )Let $\mathbb F$ be a finite Galois extension of $\mathbb K$...

Show that $f(x) = x^5 – 10x + 2 \in \mathbb Q[x]$ is not solvable by radicals.

An irreducible polynomial is inseparable iff the exponent of each irreducible factor over an algebraic closure is a multiple of the characteristic

A shorter proof of an important lemma: If $\tau$ is an transposition in $\mathscr{S}_n$ and $\phi \in \mathscr{S}_n$ then $ N(\tau\phi)=N(\phi)\pm 1$

Why does Equal Finite Disjoint Union of Cartesian Product have Common Refinement?

Which One of the Integral Expression is Always Larger?

Bounded Integral Sequence is Convergent?

Limit in Total Variation Converging to Zero Implies Absolute Continuity?

Convergence in Integral and Bounded in Lp Implies Convergence in Measure?

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