Sequences of Hopf–Swan subgroups

Let l be an odd prime which satisfies Vandiver's conjecture, let n⩾1 be an integer, and let K=Q(ζn) where ζn is a primitive lnth root of unity. Let Cl denote the cyclic group of order l. For each j, j=1,…,ln−1, there exists an inclusion of Larson orders in KCl: Λj−1⊆Λj and a corresponding surjection of Hopf–Swan subgroups T(Λj−1)→T(Λj). For the cases n=1,2 we investigate the structure of various terms in the sequence of Hopf–Swan subgroups including the Swan subgroup T(Λ0).