List questions from solvable-groups

Published on 14 Sep 2015 - 9:08

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Group of order $48$ must have a normal subgroup of order $8$ or $16$

Published on 09 Oct 2015 - 3:11

36

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If $ G $ is a finite soluble group and satisfies the permutizer condition, then for any odd prime $ p $, $ G $ is $ p $-supersoluble.

Published on 25 Mar 2026 - 9:30

58

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$H, N$ subgroups of $S_{5}$

Published on 26 Mar 2026 - 18:55

1.3k

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Question about upper central series of a group

Published on 21 Oct 2015 - 13:43

141

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show if $ G $ is supersoluble then $ G $ has a chief factor such that every chief factor of order $ p $.

Published on 21 Oct 2015 - 14:33

985

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If $G$ is a group such that any two commutators commute, $G$ is solvable

Published on 31 Oct 2015 - 23:56

58

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Why is $\Bbb{Z_2} / \{e\} = \Bbb{Z_2}$?

Published on 02 Mar 2026 - 4:22

851

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Nilpotency class of dihedral group $D_{16}$

Published on 05 Nov 2015 - 5:37

976

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Finite group is solvable iff it has a normal series with $p$-primary abelian quotient groups

Published on 02 Mar 2026 - 4:23

22

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What tools are there for specific cases of Feit-Thompson?

Published on 23 Nov 2015 - 1:45

144

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The groups with nilpotent hall $p'$ subgroup.

Published on 17 Mar 2026 - 14:33

472

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A proof that BS(1,2) is not polycyclic

Published on 03 Dec 2015 - 20:28

31

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Quotient is isomorphic exercise

Published on 06 Dec 2015 - 3:11

75

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Proof of solvability of B2 group

Published on 06 Dec 2015 - 4:24

List Question

$G$ solvable $\implies$ composition factors of $G$ are of prime order.

Group of order $48$ must have a normal subgroup of order $8$ or $16$

If $ G $ is a finite soluble group and satisfies the permutizer condition, then for any odd prime $ p $, $ G $ is $ p $-supersoluble.

$H, N$ subgroups of $S_{5}$

Question about upper central series of a group

show if $ G $ is supersoluble then $ G $ has a chief factor such that every chief factor of order $ p $.

If $G$ is a group such that any two commutators commute, $G$ is solvable

Why is $\Bbb{Z_2} / \{e\} = \Bbb{Z_2}$?

Nilpotency class of dihedral group $D_{16}$

Finite group is solvable iff it has a normal series with $p$-primary abelian quotient groups

What tools are there for specific cases of Feit-Thompson?

The groups with nilpotent hall $p'$ subgroup.

A proof that BS(1,2) is not polycyclic

Quotient is isomorphic exercise

Proof of solvability of B2 group

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