We show that the exponent is invariant under twisting. We prove that for semisimple and cosemisimple Hopf algebras H, the exponent is finite and divides dim(H). For triangular Hopf algebras in characteristic zero, we show that the exponent divides dim(H). We conjecture that if H is semisimple and cosemisimple then the exponent always divides dim(H). These theorems and conjecture are motivated by the work of Kashina [Ka], who showed that (using our language) if the exponent of H divides dim(H… CONTINUE READING