Research On Some Problems Which Are Analogous To Cohen-Lenstra Conjecture On The 2-part Of Class Groups Of Quadratic Fields

Cohen-Lenstra conjecture is a famous conjecture in algebraic number theory. Due to the description of the 2-ranks of ideal class groups of quadratic fields by the Gauss’ genus theory, Cohen-Lenstra conjecture could avoid the 2-part of class groups of quadratic fields. With the help of Pari-GP, a software used in computational num-ber theory, we calculate a number of 2-part of ideal class groups of quadratic fields and study their distributions. We also calculate the orders of the corresponding automor-phism groups and compare them to the general law from Cohen-Lenstra conjecture to find the difference between them. Furthermore, we present some conjectures on the 2-part of ideal class groups of imaginary quadratic fields.