Bourbaki

Exercise 3, § 6

Algebra, I, 147

Define extensions (cf. § 5, Exercise 10)

Z/2Z×Z/2Z→A4→A3 \mathbf{Z}/2\mathbf{Z} \times \mathbf{Z}/2\mathbf{Z} \to \mathfrak{A}_4 \to \mathfrak{A}_3
Z/2Z×Z/2Z→S4→S3. \mathbf{Z}/2\mathbf{Z} \times \mathbf{Z}/2\mathbf{Z} \to \mathfrak{S}_4 \to \mathfrak{S}_3.

Show that these extensions are non-trivial, that the first admits a section and that the second does not.

Solution

No solution has been written yet.

Transcribed from the printed volume. Not translated.