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
KEYWORD
nonn
AUTHOR
M. Farrokhi D. G., Sep 16 2020
STATUS
approved