A343822 Numbers k such that the alternating group A_k is not a Hurwitz group.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 38, 39, 40, 41, 44, 46, 47, 48, 53, 54, 55, 59, 60, 61, 62, 67, 68, 69, 74, 75, 76, 82, 83, 89, 90, 95, 97, 103, 104, 110, 111, 118, 125, 131, 139, 146, 167

Offset: 1

Author

Eric M. Schmidt, Apr 30 2021

Keywords

• nonn
• fini
• full

Comments

Complement of A343821.

See the classification in section 5 of the first Conder reference. The term 139 is erroneously omitted there, as pointed out in the second Conder reference [Section 3].

Links

• Marston D. E. Conder, Generators for alternating and symmetric groups, J. London Math. Soc. (2) 22 (1980), pp. 75-86.
• Marston D. E. Conder, Some results on quotients of triangle groups, Bulletin of the Australian Mathematical Society, Volume 30, Issue 1, August 1984, pp. 73-90.
• J. J. Etayo Gordejuela and E. Martínez, Alternating groups, Hurwitz groups and H^*-groups, Journal of Algebra, 283 (2005), pp. 327-349.

Crossrefs

Cf. A179982, A343821.