A340514 - OEIS

A340514

a(n) is the minimal order of a group in which all groups of order n can be embedded.

1, 2, 3, 8, 5, 12, 7, 32, 27, 20, 11, 144, 13, 28, 15, 256, 17, 216, 19, 160, 63, 44, 23

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OFFSET

1,2

REFERENCES

Heffernan, Robert, Des MacHale, and Brendan McCann. "Cayley's Theorem Revisited: Embeddings of Small Finite Groups." Mathematics Magazine 91.2 (2018): 103-111.

LINKS

Table of n, a(n) for n=1..23.

Heffernan, Robert, Des MacHale, and Brendan McCann, Minimal embeddings of small finite groups, arXiv:1706.09286 [math.GR], Jun 28 2017.

MathStackExchange, How powerful is Cayley's theorem?, Oct 07 2021.

FORMULA

From David A. Craven, Oct 07 2021: (Start)

a(p)=p, a(p^2)=p^3, a(p^3)=p^6 if p is odd, a(8)=32.

If p<q are distinct primes, a(pq)=p^2q if p divides (q-1), a(pq)=pq otherwise. (End)

CROSSREFS

Cf. A000001, A340515.

Sequence in context: A066959 A344368 A342768 * A086471 A328846 A249154

Adjacent sequences: A340511 A340512 A340513 * A340515 A340516 A340517

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Feb 02 2021

EXTENSIONS

a(16)-a(23) from David A. Craven, Oct 07 2021

STATUS

approved