OFFSET
1,4
COMMENTS
See Slattery references for a precise definition of similarity.
See Betz and Nash first reference for proof of the first 22 terms.
See Betz and Nash second reference for proof of terms 23--49.
LINKS
Alexander Betz and David A. Nash, Classifying groups with a small number of subgroups, arXiv:2006.11315 [math.GR], (2020).
Alexander Betz and David A. Nash, A note on abelian groups with fewer than 50 subgroups, preprint, (2020).
G. A. Miller, Groups having a small number of subgroups, Proc. Natl. Acad. Sci. U S A, vol. 25 (1939) 367-371.
M. C. Slattery, On a property motivated by groups with a specified number of subgroups, Amer. Math. Monthly, 123 (2016), 78-81.
M. C. Slattery, Groups with at most twelve subgroups, arXiv:1607.01834 [math.GR], 2016-2020.
EXAMPLE
For n = 6, a(6) = 3 and the three similarity classes of abelian groups with exactly six subgroups are Z_{p^5}, Z_{p^2q}, and Z_3 X Z_3.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
David A. Nash, Jun 29 2020
STATUS
approved