Exercises in the literature

Exercises related to permutations on a 16-set:

See Introduction to the Theory of Groups of Finite Order, by Robert D. Carmichael (1937), reprinted by Dover Books, 1956.

See especially
pp. 42-43, ex. 30 and 31;
p. 73, ex. 32;
p. 165, ex. 20;
p. 304, ex. 3;
pp. 320-321, ex. 7-12;
pp. 336-337, ex. 4-7, 9, 10;
p. 353, ex. 5;
p. 392, ex. 6, part (3);
p. 437, ex. 14-17;
p. 439, ex. 11-12;
p. 440, ex. 20.

These exercises in Carmichael have a simplicity and clarity lacking in many more recent works on finite mathematics.

For a related discussion of a 16-set in the literature, see "Generalized Steiner Systems of Type 3-(v,{4,6},1)," by E. F. Assmus, Jr., and J. E. Novillo Sardi, in Finite Geometries and Designs, edited by P. J. Cameron, J. W. P. Hirschfeld, and D. R. Hughes, Cambridge University Press, 1981.