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Let

G

be finite group and

\mathcal{K}

a conjugacy class of

G

that generates

G

. Prove that the following two statements are equivalent: (1) There exists a positive integer

m

such that every element of

G

can be written as a product of

m

(not necessarily distinct) elements of

\mathcal{K}

. (2)

G

is equal to its own commutator subgroup. J. Denes

Problem Statement