Nonexistence conjecture for elementary abelian class groups

For an odd prime $p$, an elementary abelian $p$-group is a group isomorphic to $(\mathbb{Z}/p\mathbb{Z})^r$. Nonexistence conjecture for elementary abelian class groups. No elementary abelian $p$-group of rank at least $3$ occurs as the class group of an imaginary quadratic field. The conjecture is motivated by the observed absence of such groups in the computed tables, including $(\mathbb{Z}/p\mathbb{Z})^3$ for all odd primes $p<100$ examined in the paper. Its resolution status is not specified here.