MathDB

Let

G

be a non-solvable finite group and let

\varepsilon > 0

. Show that there exist a positive integer

k

and a word

w\in F_k

such that

w

assumes the value

1

with probability less than

\varepsilon

when its

k

arguments are considered to be independent and uniformly distributed random variables with values in

G

. (We write

F_k

for the free group generated by

k

elements.)

Problem Statement