Generalizations of results of Friedman and Washington on cokernels of random p-adic matrices

Let p be prime and X a Haar-random n × matrix over Z , the ring of -adic integers. P 1 ( t ) … l ∈ [ ] monic polynomials degree at most 2 whose images modulo are distinct irreducible in F where denotes finite field elements. For each j let G module / . We show that as goes to infinity, probabilities cok ≃ independent, probability can described terms Cohen–Lenstra distribution. also for any fixed is constant multiple ¯ an uniformly random These results generalize work Friedman Washington prove new cases conjecture Cheong Huang.