A337706 Possible values for the product of the orders of all elements of a finite group.

1, 2, 8, 9, 32, 72, 128, 512, 625, 648, 2048, 6561, 8192, 20000, 32768, 41472, 52488, 117649, 131072, 524288, 2654208, 3359232, 4782969, 8388608, 12500000, 15059072, 33554432, 134217728, 214990848, 536870912, 2147483648, 2448880128

Offset

1,2

Comments

The product of the orders of all elements of a finite group G is denoted by P(G).

P(A X B) = P(A)^|B|P(B)^|A| for finite groups A and B of coprime orders.

P(G) < P(C_n) for every noncyclic finite group G of order n.

Links

M. Farrokhi D. G., Table of n, a(n) for n = 1..2733

M. Garonzi and M. Patassini, Inequalities detecting structural properties of a finite group, Comm. Algebra (2017) 45(2), 677-687.

M. Herzog, P. Longobardi, and M. Maj, Properties of finite and periodic groups determined by their element of orders (a survey), Group theory and computation, 59-90, Indian Stat. Inst. Ser., Springer, Singapore, 2018.

Example

P(C_6) = 1*2*3*3*6*6 = 648.

Prog

(GAP) Product(List(G, Order))

Crossrefs

Sequence in context: A166968 A075644 A088825 * A368341 A369649 A181887

Adjacent sequences: A337703 A337704 A337705 * A337707 A337708 A337709

Keyword

nonn

Author

M. Farrokhi D. G., Sep 16 2020

Status

approved