A349930 - OEIS

A349930

a(n) is the number of groups of order A340511(n) which have no subgroup of order d, for some divisor d of A340511(n).

1, 1, 3, 2, 1, 2, 7, 1, 1, 2, 3

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OFFSET

1,3

COMMENTS

Also, number of NCLT groups of order A340511(n); NCLT means "Non-Converse Lagrange Theorem" because the converse to Lagrange's theorem does not hold for the groups of this sequence.

All terms up to a(11) come from Curran's link.

LINKS

Table of n, a(n) for n=1..11.

M. J. Curran, Non-CLT groups of small order, Comm. Algebra 11 (1983), 111-126.

Des MacHale and J. Manning, Converse Lagrange Theorem Orders and Supersolvable Orders, Journal of Integer Sequences, 2016, Vol. 19, #16.8.7.

Index entries for sequences related to groups.

EXAMPLE

A340511(1) = 12, and there is only one group of order 12: Alt(4) = A_4 which has no subgroup of order d = 6, despite the fact that 6 divides 12, hence a(1) = 1.

A340511(3) = 36, and there are 3 such NCLT groups of order 36: one group (C_3)^2 X C_4 has no subgroup of order 12, and the two groups A_4 X C_3 and (C_2)^2 X C_9 have no subgroup of order 18, hence a(3) = 3.

CROSSREFS

Cf. A000001, A340511, A341048.

Sequence in context: A136531 A127318 A362689 * A274512 A175947 A085068

Adjacent sequences: A349927 A349928 A349929 * A349931 A349932 A349933

KEYWORD

nonn,more

AUTHOR

Bernard Schott, Dec 05 2021

STATUS

approved