List questions from solvable-groups

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If $G$ is solvable and $G/[G,G]$ is cyclic, can $G\times G$ be generated by 2 elements?

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On the Hall Theorem

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Prove that $F(\sqrt{\alpha}) = F(\sqrt{\beta})$

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Why is a finite group, with a maximal subgroup which is abelian, soluble?

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A group of order less than $60$

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Proof with solvable groups

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nilpotent group implies solvable group

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Homomorphic Image

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Nilpotent group with torsion divisible abelian quotient

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List Question

A question on solvable groups.

If $G$ is solvable and $G/[G,G]$ is cyclic, can $G\times G$ be generated by 2 elements?

An alternative definition of a solvable group

How to prove that $G/(H \cap K)$ is solvable given $H \triangleleft G, K \triangleleft G$ and both $G/H$ and $G/K$ are solvable using Abel series?

Are the groups of order $p^3q^5$ solvable?

On the Hall Theorem

Prove that $F(\sqrt{\alpha}) = F(\sqrt{\beta})$

Clarification of Abel-Ruffini theorem statement

Why is a finite group, with a maximal subgroup which is abelian, soluble?

A group of order less than $60$

Proof with solvable groups

Subgroup of solvable group is solvable (not using tower definition)

nilpotent group implies solvable group

Homomorphic Image

Nilpotent group with torsion divisible abelian quotient

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