Question

Is $p(x^n)$ solvable by radicals if $p(x)$ is solvable by radicals?

score 47 · Answer 1 · 2023-12-18 10:24:55

47

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Is $p(x^n)$ solvable by radicals if $p(x)$ is solvable by radicals?

Published on 18 Dec 2023 - 10:24

score 125 · Answer 2 · 2023-12-21 19:19:12

125

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Let $G$ be a finite group and $f$ a non-trivial automorphism of $G$ such that for each $x\in G, f(x)=x$ or $f(x)=x^{-1}$. Prove that $G$ is solvable.

Published on 21 Dec 2023 - 19:19

score 169 · Answer 3 · 2024-01-06 07:53:23

169

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Is $SL_2(\mathbb{C})$ a solvable group?

Published on 06 Jan 2024 - 7:53

score 68 · Answer 4 · 2026-03-25 16:03:15

68

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Proof of a particular piece of Milnor-Wolf theorem

Published on 25 Mar 2026 - 16:03

score 21 · Answer 5 · 2024-02-29 15:16:16

21

Views

Main idea of the proof of the Galois solvability criterion

Published on 29 Feb 2024 - 15:16

score 121 · Answer 6 · 2026-03-26 01:03:17

121

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Equivalent Definition of Solvable Groups in Serre’s Book

Published on 26 Mar 2026 - 1:03

score 38 · Answer 7 · 2024-03-21 11:24:52

38

Views

What is the least degree polynomial whose Galois group is not solvable in the field of Bring rational numbers?

Published on 21 Mar 2024 - 11:24

score 257 · Answer 8 · 2015-01-08 23:51:42

257

Views

Reconciling Different Definitions of Solvable Group

Published on 08 Jan 2015 - 23:51

score 153 · Answer 9 · 2015-01-09 16:42:02

153

Views

What is set builder of $\langle H, K \rangle$?

Published on 09 Jan 2015 - 16:42

score 896 · Answer 10 · 2015-01-17 21:22:52

896

Views

Prove $G$ is cyclic if for every $n\in \Bbb{N}$, there are at most $n$ solutions to the equation $x^n=e$.

Published on 17 Jan 2015 - 21:22

score 1.3k · Answer 11 · 2026-03-26 12:52:54

1.3k

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Some solvable Lie algebra but not nilpotent

Published on 26 Mar 2026 - 12:52

score 816 · Answer 12 · 2015-03-02 19:37:39

816

Views

Ideals of solvable lie algebra

Published on 02 Mar 2015 - 19:37

score 731 · Answer 13 · 2015-03-13 08:28:05

731

Views

Subgroups of smallest possible index in a solvable group

Published on 13 Mar 2015 - 8:28

score 793 · Answer 14 · 2015-03-17 23:51:42

793

Views

Solvable groups

Published on 17 Mar 2015 - 23:51

score 357 · Answer 15 · 2015-03-19 05:24:12

357

Views

How can I tell if $x^5 - (x^4 + x^3 + x^2 + x^1 + 1)$ is/is not part of the solvable group of polynomials?

Published on 19 Mar 2015 - 5:24

List Question

Is $p(x^n)$ solvable by radicals if $p(x)$ is solvable by radicals?

Let $G$ be a finite group and $f$ a non-trivial automorphism of $G$ such that for each $x\in G, f(x)=x$ or $f(x)=x^{-1}$. Prove that $G$ is solvable.

Is $SL_2(\mathbb{C})$ a solvable group?

Proof of a particular piece of Milnor-Wolf theorem

Main idea of the proof of the Galois solvability criterion

Equivalent Definition of Solvable Groups in Serre’s Book

What is the least degree polynomial whose Galois group is not solvable in the field of Bring rational numbers?

Reconciling Different Definitions of Solvable Group

What is set builder of $\langle H, K \rangle$?

Prove $G$ is cyclic if for every $n\in \Bbb{N}$, there are at most $n$ solutions to the equation $x^n=e$.

Some solvable Lie algebra but not nilpotent

Ideals of solvable lie algebra

Subgroups of smallest possible index in a solvable group

Solvable groups

How can I tell if $x^5 - (x^4 + x^3 + x^2 + x^1 + 1)$ is/is not part of the solvable group of polynomials?

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