We investigate the complexity of several decision, enumeration and counting problems in axiom pinpointing in Description Logics. We prove hardness results that already hold for the propositional Horn fragment. We show that for this fragment, unless p = np, all minimal subsets of a given TBox that have a given consequence, i.e. MinAs, cannot be enumerated in a specified lexicographic order with ...

Let G be a finite group having a normal p-subgroup N that contains its centralizer CG(N), and let R be a p-adic ring. It is shown that any finite p-group of units of augmentation one in RG which normalizes N is conjugate to a subgroup of G by a unit of RG, and if it centralizes N it is even contained in N .

It has been shown that for distinct odd primes p1, p2, . . . , pn and q, all Moufang loops of order p1p2 · · · pnq are groups if and only if q is not congruent to 1 modulo pi for each i. In this paper, we extend that result to include Moufang loops of order p1p 2 2 · · · pnq. Mathematics Subject Classification: 20N05