In [1], J.H.E. Cohn defined a{G) to be the smallest integer n such that the group G is the set-theoretic union of n proper subgroups. A number of re-sults were proved for soluble groups leading to the conjecture that if G is a finite noncyclic soluble group then a{G) = p" + 1, where pa is the order of a particular chief factor of G. It was also conjectured that there is no group G for which a{G) = 7. It is well known that a{G) can never be equal to 2 and 7 is the next integer not of the form/1 + 1.
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