Question

Standard reference for Kaluzhnin's theorem

score 104 · Answer 1 · 2013-12-31 11:50:22

104

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Standard reference for Kaluzhnin's theorem

Published on 31 Dec 2013 - 11:50

score 589 · Answer 2 · 2014-01-02 15:11:26

589

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Show that the minimal polynomial of every element in $K=\mathbb{Q}(\zeta)$ is solvable by radicals, where $\zeta$ is a primitive 9th root of unity.

Published on 02 Jan 2014 - 15:11

score 1.4k · Answer 3 · 2014-01-05 08:19:00

1.4k

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Prove that if a group is nilpotent , then its quotient with its Frattini subgroup is abelian

Published on 05 Jan 2014 - 8:19

score 106 · Answer 4 · 2014-01-07 08:00:04

106

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If the product $x_1x_2...x_n=1$, prove that each $x_i=1$.

Published on 07 Jan 2014 - 8:00

score 367 · Answer 5 · 2014-01-07 10:59:18

367

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Maximal subgroups of direct product of solvable groups

Published on 07 Jan 2014 - 10:59

score 871 · Answer 6 · 2014-01-19 00:26:50

871

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Why is a group of order 135 nilpotent?

Published on 19 Jan 2014 - 0:26

score 3.6k · Answer 7 · 2014-01-30 12:21:54

3.6k

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Understanding non-solvable algebraic numbers

Published on 30 Jan 2014 - 12:21

score 51 · Answer 8 · 2014-02-18 00:00:51

51

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Non-solvable, closed subgroups of $\mathrm{PSL}(2,\mathbb{R})$

Published on 18 Feb 2014 - 0:00

score 157 · Answer 9 · 2014-02-26 02:53:37

157

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Finding a particular chief series for a supersolvable group

Published on 26 Feb 2014 - 2:53

score 1.4k · Answer 10 · 2026-03-25 21:26:27

1.4k

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Finite groups with all maximal subgroups of prime power index are solvable?

Published on 25 Mar 2026 - 21:26

score 641 · Answer 11 · 2017-04-16 14:41:50

641

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two equivalent definitions for solvable groups

Published on 16 Apr 2017 - 14:41

score 1.8k · Answer 12 · 2017-04-18 21:18:53

1.8k

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Why does "solvability" for groups suggest something about the solution of polynomials?

Published on 18 Apr 2017 - 21:18

score 517 · Answer 13 · 2017-04-24 16:36:51

517

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Prove that G is a solvable group

Published on 24 Apr 2017 - 16:36

score 266 · Answer 14 · 2017-04-25 09:01:11

266

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$L/k$ finite Galois extension with solvable Galois group divisible by a prime $p$ . Does there exist field $k\subseteq F \subseteq L$ s.t. $p=[F:k]$?

Published on 25 Apr 2017 - 9:01

score 943 · Answer 15 · 2017-04-25 09:26:21

943

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$f(x)$ irreducible over $\mathbb Q$ of prime degree ; then Galois group of $f$ is solvable iff $L=\mathbb Q(a,b)$ for any two roots $a,b$ of $f$?

Published on 25 Apr 2017 - 9:26

List Question

Standard reference for Kaluzhnin's theorem

Show that the minimal polynomial of every element in $K=\mathbb{Q}(\zeta)$ is solvable by radicals, where $\zeta$ is a primitive 9th root of unity.

Prove that if a group is nilpotent , then its quotient with its Frattini subgroup is abelian

If the product $x_1x_2...x_n=1$, prove that each $x_i=1$.

Maximal subgroups of direct product of solvable groups

Why is a group of order 135 nilpotent?

Understanding non-solvable algebraic numbers

Non-solvable, closed subgroups of $\mathrm{PSL}(2,\mathbb{R})$

Finding a particular chief series for a supersolvable group

Finite groups with all maximal subgroups of prime power index are solvable?

two equivalent definitions for solvable groups

Why does "solvability" for groups suggest something about the solution of polynomials?

Prove that G is a solvable group

$L/k$ finite Galois extension with solvable Galois group divisible by a prime $p$ . Does there exist field $k\subseteq F \subseteq L$ s.t. $p=[F:k]$?

$f(x)$ irreducible over $\mathbb Q$ of prime degree ; then Galois group of $f$ is solvable iff $L=\mathbb Q(a,b)$ for any two roots $a,b$ of $f$?

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