For larger orders, implement one of the randomized algorithms below:
S. Bratus and I. Pak, “Fast Constructive Recognition of a Black Box Group Isomorphic to Sn or An using Goldbach’s Conjecture,” Journal of Symbolic Computation, vol. 29, no. 1, pp. 33–57, Jan. 2000, doi: 10.1006/jsco.1999.0295.
R. Beals, C. R. Leedham-Green, A. C. Niemeyer, C. E. Praeger, and A. K. Seress, “A BLACK-BOX GROUP ALGORITHM FOR RECOGNIZING FINITE SYMMETRIC AND ALTERNATING GROUPS, I,” p. 17.
S. Jambor, M. Leuner, A. C. Niemeyer, and W. Plesken, “Fast recognition of alternating groups of unknown degree,” Journal of Algebra, vol. 392, pp. 315–335, Oct. 2013, doi: 10.1016/j.jalgebra.2013.06.005.
For larger orders, implement one of the randomized algorithms below:
S. Bratus and I. Pak, “Fast Constructive Recognition of a Black Box Group Isomorphic to Sn or An using Goldbach’s Conjecture,” Journal of Symbolic Computation, vol. 29, no. 1, pp. 33–57, Jan. 2000, doi: 10.1006/jsco.1999.0295.
R. Beals, C. R. Leedham-Green, A. C. Niemeyer, C. E. Praeger, and A. K. Seress, “A BLACK-BOX GROUP ALGORITHM FOR RECOGNIZING FINITE SYMMETRIC AND ALTERNATING GROUPS, I,” p. 17.
S. Jambor, M. Leuner, A. C. Niemeyer, and W. Plesken, “Fast recognition of alternating groups of unknown degree,” Journal of Algebra, vol. 392, pp. 315–335, Oct. 2013, doi: 10.1016/j.jalgebra.2013.06.005.