cp's OEIS Frontend

A274847 a(n) = number of similarity classes of groups with exactly n subgroups (see reference for precise definition of similarity classes).

%I A274847 #37 Mar 09 2024 11:05:00
%S A274847 1,1,1,2,2,5,1,7,2,12,4,11,1,17,8,22,3,22,5
%N A274847 a(n) = number of similarity classes of groups with exactly n subgroups (see reference for precise definition of similarity classes).
%C A274847 See Slatterly references for precise definition of similarity classes and a proof of the first 12 terms.
%C A274847 See Betz and Nash for correction of a(10) and proof of terms 13-19.
%H A274847 Alexander Betz and David A. Nash, <a href="https://arxiv.org/abs/2006.11315">Classifying groups with a small number of subgroups</a>, arXiv:2006.11315 [math.GR], 2020.
%H A274847 Angsuman Das and Arnab Mandal, <a href="https://arxiv.org/abs/2403.01262">Solvability of a group based on its number of subgroups</a>, arXiv:2403.01262 [math.GR], 2024.
%H A274847 George A. Miller, <a href="http://www.pnas.org/content/25/7/367.full.pdf">Groups having a small number of subgroups</a>, Proc. Natl. Acad. Sci. U S A, vol. 25 (1939) 367-371.
%H A274847 David A. Nash and Alexander Betz, <a href="https://arxiv.org/abs/2006.11315">Classifying groups with a small number of subgroups</a>, arXiv:2006.11315 [math.GR], 2020.
%H A274847 Michael C. Slattery, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.123.1.78">On a property motivated by groups with a specified number of subgroups</a>, Amer. Math. Monthly, 123 (2016), 78-81.
%H A274847 Michael C. Slattery, <a href="http://arxiv.org/abs/1607.01834">Groups with at most twelve subgroups</a>, arXiv:1607.01834 [math.GR], 2016.
%e A274847 For n = 6 the a(6) = 5 similarity classes of groups with 6 subgroups are Z_{p^5}, Z_p X Z_{q^2}, Z_3 X Z_3, S_3, Q_8.
%Y A274847 Cf. A018216, A289445.
%K A274847 nonn,more
%O A274847 1,4
%A A274847 _Michael C Slattery_, Jul 08 2016
%E A274847 Correction of a(10) and extension to 19 terms by _David A. Nash_, Jun 29 2020