The cycle index of the symmetric group S in its natural action is given by the formula:

The symmetric group S has the following multiplication table.

An element of order 6 in the group S can be written in cycle notation as (1 2) (3 4 5).

The center of the symmetric group S is trivial for n 3.

The table of marks for the symmetric group S on 3 letters:

(and also the symmetric group S) on 4 letters.

A recursively presented simple group S has solvable word problem.

I also want to point out once again that our group' s official position now is to have as few amendments as possible.

Now to my group' s stand on the Katiforis report.

The group S is solvable if and only if n â 4.