List questions from solvable-groups

Published on 30 Dec 2020 - 23:08

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Proof easy version of Burnside's Lemma

Published on 06 Jan 2021 - 5:53

239

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The degree of an irreducible representation of a finite solvable group

Published on 18 Jan 2021 - 11:32

187

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If $G$ is a finite group such that every maximal subgroup is nilpotent, are any two maximal subgroups of $G$ conjugate?

Published on 25 Mar 2026 - 13:56

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Extensions of solvable Groups and solvability in between...

Published on 26 Mar 2026 - 11:07

34

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Why do certain relatively free groups have perfect commutator subgroups?

Published on 23 Feb 2026 - 5:50

127

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Show that a group of order $2^2 \cdot 5 \cdot 23^r$ is solvable but not simple.

Published on 14 Feb 2021 - 5:06

88

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Prove that $G$ is solvable group without using Burnside Theorem.

Published on 18 Feb 2021 - 19:02

49

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Let $G$ be solvable. Let $g\in G$. What can we say about $g=[g^{x_1}, g^{y_1}]\dots [g^{x_n}, g^{y_n}]$ with $x_i,y_i\in G,i=1,...,n$?

Published on 03 Mar 2021 - 19:37

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Show that any group of order 294 is solvable.

Published on 12 Mar 2021 - 6:36

217

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Show that every group of order $4125=3\cdot 5^3\cdot 11$ is solvable.

Published on 12 Mar 2021 - 15:38

302

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Proving a group of order $35^3$ is solvable

Published on 27 Mar 2021 - 19:32

110

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Non-abelian solvable group of order $p^2q$ that including no subgroup of order $pq$.

Published on 30 Mar 2021 - 21:24

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the example of field extension over $\mathbb{Q}_p$ such that the Galois group is not solvable

Published on 26 Mar 2026 - 20:44

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Are all simple groups solvable?

Published on 05 Apr 2021 - 13:50

List Question

A minimal normal group of a solvable group is abelian

Proof easy version of Burnside's Lemma

The degree of an irreducible representation of a finite solvable group

If $G$ is a finite group such that every maximal subgroup is nilpotent, are any two maximal subgroups of $G$ conjugate?

Extensions of solvable Groups and solvability in between...

Why do certain relatively free groups have perfect commutator subgroups?

Show that a group of order $2^2 \cdot 5 \cdot 23^r$ is solvable but not simple.

Prove that $G$ is solvable group without using Burnside Theorem.

Let $G$ be solvable. Let $g\in G$. What can we say about $g=[g^{x_1}, g^{y_1}]\dots [g^{x_n}, g^{y_n}]$ with $x_i,y_i\in G,i=1,...,n$?

Show that any group of order 294 is solvable.

Show that every group of order $4125=3\cdot 5^3\cdot 11$ is solvable.

Proving a group of order $35^3$ is solvable

Non-abelian solvable group of order $p^2q$ that including no subgroup of order $pq$.

the example of field extension over $\mathbb{Q}_p$ such that the Galois group is not solvable

Are all simple groups solvable?

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