A270368 a(n) = order of the n-th Zassenhaus nearfield.

25, 121, 49, 529, 121, 841, 3481

Offset

1,1

Comments

Let p be a prime and G a subgroup of the general linear group GL(d,p) acting transitively on the nonzero vectors of the d-dimensional vector space (F(p))^d over the finite field F(p) with p elements. Assume that G contains a sharply transitive set. Then p^d is in the sequence and G is one of the seven finite sharply transitive linear groups of Zassenhaus (see "Sporadic finite transitive linear groups" in Wikipedia link).

Links

Table of n, a(n) for n=1..7.

Wikipedia, List of transitive finite linear groups

Prog

(Magma) [ZassenhausNearfield(n): n in [1..7]];

Crossrefs

See A374524 for another version.

Sequence in context: A124953 A126412 A078815 * A206472 A036057 A083509

Adjacent sequences: A270365 A270366 A270367 * A270369 A270370 A270371

Keyword

nonn,more

Author

Arkadiusz Wesolowski, Mar 15 2016

Status

approved