MathDB

Prove that there exists a constant

c>0

such that in every nontrivial finite group

G

there exists a sequence of length at most

c\ln |G|

with the property that each element of

G

equals the product of some subsequence. (The elements of

G

in the sequence are not required to be distinct. A subsequence of a sequence is obtained by selecting some of the terms, not necessarily consecutive, without reordering them; for example,

4,4,2

is a subesequence of

2,4,6,4,2,

but

2,2,4

is not.)

Problem Statement