

A337706


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


1



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
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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)^BP(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), 677687.
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, 5990, 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 * A181887 A221049 A181476
Adjacent sequences: A337703 A337704 A337705 * A337707 A337708 A337709


KEYWORD

nonn


AUTHOR

M. Farrokhi D. G., Sep 16 2020


STATUS

approved



