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Abstract Algebra

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Semidirect Properties

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Which of the following statements are true about semidirect products?

Select ALL that apply.

A

The semidirect product of two abelian groups is an abelian group.

B

If the semidirect product of two groups is abelian, both groups must be abelian.

C

Every group is a semidirect product of some of its nontrivial subgroups.

D

The semidirect product of two cyclic groups needs not be a cyclic group.

E

If the semidirect product of two groups is cyclic, both groups must be cyclic.