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A270368 a(n) = order of the n-th Zassenhaus nearfield. 0

%I #9 Sep 08 2022 08:46:16

%S 25,121,49,529,121,841,3481

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

%C 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).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/List_of_transitive_finite_linear_groups">List of transitive finite linear groups</a>

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

%K nonn,more

%O 1,1

%A _Arkadiusz Wesolowski_, Mar 15 2016

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Last modified March 2 21:08 EST 2024. Contains 370498 sequences. (Running on oeis4.)