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Abstract Algebra

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Moderate

Semidirectly Decomposable groups

ABSALG-1DFWYL

Which of the following groups is NOT the semidirect product of two of its nontrivial subgroups?

A

The group $S_3$ of permutation on three symbols.

B

The group $A_4$ of even permutations on four symbols.

C

The group $D_4$ of symmetries of a square.

D

The group $A_5$ of even permutation on four symbols.​