A fresh approach to the exceptional automorphism and covers of the symmetric groups

الملخص EN

The outer auto orphism of the symmetric group S6 and the triple covers of the alternating groups A6 and A7 are fascinating examples of familiar objects exhibiting exceptional behavior.

Not surprisingly they can be used to ‘explain’ the existence of much larger sporadic groups.

In this paper we use the techniques of symmetric generation to construct S6 : 2, 3˙S6 and 3˙S7 in an elementary and revealing fashion.