List questions from solvable-groups

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Are there more even or odd groups?

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Group with all Sylow subgroups cyclic (exercise 5C.4 of "Finite group theory", Isaacs).

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Are there irreducible polynomials that are partially solvable by radicals?

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Direct product of two nilpotent groups is nilpotent and direct product of two solvable groups is solvable

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For every group of odd order, is $F(\omega(G))$ abelian?

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G torsion-free, $H \leq G$ and $[G:H] < \infty$ imply equal nilpotent classes

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139

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Group of order $3^k5^l$ is solvable

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A difficulty in understanding Proposition 10. in Dummit & Foot p.195

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Variations on Hall Theorem for solvability in Dummit and Foote

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A group is solvable if it has only one $p$-Sylow subgroup for each $p$

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Affine type primitive group

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If $G_f\cong D_5$ for $f(x)=x^5+ax+b\in \mathbb{Q}[x]$, show that these criteria are true.

Published on 27 Mar 2023 - 16:45

List Question

A finite nilpotent group has supersolvable series

Are there more even or odd groups?

Group with all Sylow subgroups cyclic (exercise 5C.4 of "Finite group theory", Isaacs).

Are there irreducible polynomials that are partially solvable by radicals?

Direct product of two nilpotent groups is nilpotent and direct product of two solvable groups is solvable

For every group of odd order, is $F(\omega(G))$ abelian?

G torsion-free, $H \leq G$ and $[G:H] < \infty$ imply equal nilpotent classes

Group of order $3^k5^l$ is solvable

A difficulty in understanding Proposition 10. in Dummit & Foot p.195

Is Z3 a Simple and Solvable groups?

Quotient of solvable groups is solvable - what's wrong with this proof?

Variations on Hall Theorem for solvability in Dummit and Foote

A group is solvable if it has only one $p$-Sylow subgroup for each $p$

Affine type primitive group

If $G_f\cong D_5$ for $f(x)=x^5+ax+b\in \mathbb{Q}[x]$, show that these criteria are true.

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