A371022 - OEIS

A371022

Numbers k with the property that there is a finite set W of groups of order divisible by k such that if k divides the order of a group G, then G has a subgroup isomorphic to a group in W.

%I #15 Mar 30 2024 11:21:10

%S 2,3,4,5,6,7,8,9,10,11,13,16,17,19,23,25,27,29,31,32,34,37,41,43,47,

%T 49,50,53,59,61,64,67,71,73,79,81,83,89,97,101,103,107,109,113,121,

%U 125,127,128,131,137,139,149,151,157,163,167,169,173,179,181,191,193,197,199

%N Numbers k with the property that there is a finite set W of groups of order divisible by k such that if k divides the order of a group G, then G has a subgroup isomorphic to a group in W.

%C These are called Cauchy numbers in Cameron et al., where they are proved to be the following set: 6 U prime powers U numbers of the form 2*p^a where p is a Fermat prime greater than 3.

%H Peter J. Cameron, David Craven, Hamid Reza Dorbidi, Scott Harper, and Benjamin Sambale, <a href="https://arxiv.org/abs/2311.15652">Minimal Cover Groups</a>, arXiv:2311.15652 [math.GR], 2023-2024.

%Y Cf. A000961, A019434.

%K nonn,easy

%O 1,1

%A _Tom Harris_, Mar 08 2024