Cayley proved that every discrete group of order \(n\) can be found in the product table for \(S_{n}\). Illustrate this result for \(S_{3}\) (Table 1.5 or Table 1.6). What does your result say about the number of distinct groups of order 3 ?

Transcribed Image Text:

Table 1.5 The 32 group (order 6) E A B C D F E E A B C F A A E F C B B B D E F A C C C F D E B A D D B C A F E F F C A B E D