schur’s exponent conjecture — counterexamples of exponent 5 and exponent 9

There is a long-standing conjecture attributed to i. schur that if g is a finite group with schur multiplier m(g) then the exponent of m(g) divides the exponent of g. it is easy to show that this is true for groups g of exponent 2 or exponent 3, but it has been known since 1974 that the conjecture fails for exponent 4. bayes, kautsky and wamsley [1] give an example of a group g of order 268 with exponent 4, where m(g) has exponent 8. (bayes, kautsky and wamsley are heros of the early days of computing with finite p-groups.) however the truth or otherwise of this conjecture has remained open up till now for groups of odd exponent, and in particular it has remained open for groups of exponent 5 and exponent 9. for a survey article on schur’s conjecture see thomas [6].