W is free if (with the above notation) Aut(C/W) = fl B(w). wE W The next lemma (which we include for completeness, but which we shall not really use), shows that free covers are completely determined by the fibre and binding groups, together with the canonical homomorphisms.
We claim this is non-split (and so Aut(Ci) is a non-split extension of G by an elementary abelian p-group). 5, if 1r1 is split then the fibre group at wo is the product of the binding group at wo with a homomorphic image of X. But this is clearly impossible. 2 Digraph coverings In this section we summarise the theory of coverings of digraphs, as developed in [23]. This will provide us with examples of finite covers with finite kernels. The construction is very closely related to the topological notion of a covering space.
E) The countable, universal, homogeneous local order D has no strong type. For any x E L the only posssibility for pI{x} would be the in-vertices, or the out-vertices of x (by homogeneity). But no point dominates, or is dominated by a cycle, and so (ii) is impossible to satisfy with either of these. Remark. There is a related notion due to Ivanov. 1 hold with respect to all types, not just 1-types. 4 here.