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

1,2

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

Table of n, a(n) for n=1..66.

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.

Sequence in context: A320230 A076564 A325044 * A303550 A164563 A179892

Adjacent sequences: A343819 A343820 A343821 * A343823 A343824 A343825

Keyword

nonn,fini,full

Author

Eric M. Schmidt, Apr 30 2021

Status

approved