The Theorem that Won the War: Activities for Part 3.2 (Rejewski's Theorems)

1. Verify the Enigma Theorem for the products of proper involutions in the activities for Part 3.1.
   (That is, for the products \(\sigma\tau \), \(\alpha\beta \), \(\mu\nu \), and \(\kappa\lambda \) in activities 2, 3, 4, and 5 of Part 3.2, respectively.)
2. Let \(E_{1}\), \(E_{2}\) be proper involution on six elements, where \(E_{2}E_{1} = (ade)(bcf)\).
   1. Find the possibilities for the involutions \(E_{1}\), \(E_{2}\).
   2. Find \(E_{1}\), \(E_{2}\).

Return to the overview of Part 3.2 (Rejewski's Theorems.

Continue to the overview of Part 3.3 (Breaking the Full Enigma).