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Moderate

Solvable Group: Characterization in Terms of Series of Subgroups

ABSALG-S4YTEP

Let $G$ be a finite group with neutral element $e$.

Which of the following properties of $G$ is not equivalent to $G$ being solvable?

A

$G$ has a normal series with abelian factors.

B

$G$ has a subnormal series with strict inclusions and factors that are cyclic of prime order.

C

$G$ has a derived series which terminates in the trivial group $\{e\}$.

D

$G$ has a subnormal series with abelian factors.

E

$G$ has a derived series which terminates in the trivial group $\{e\}$ and has factors that are cyclic of prime order.