Kuo, WentangLiu, Yu-Ru2023-10-032023-10-032008https://doi.org/10.1090/crmp/046http://hdl.handle.net/10012/19995Abstract. We give a survey of the Erd}o-Kac theorem and its various generalizations. In particular, we discuss an open conjecture of Erd}os and Pomerance about the distribution of the number of distinct prime divisors of the order of a xed integer in the multiplicative groups (Z=nZ) . We also formulate a Carlitz module analogue of this conjecture and provide a sketch of its proof.enBook Chapter