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W and the latter has (non-trivial) simple fibre groups. 1), so these groups are non-trivial and 7r2 is nontrivial. 4 that ire is free or superlinked. 4 in the fomer case, and by hypothesis in the latter). Thus there is a closed subgroup H of Aut(C) with H fl Aut(C/W) = Aut(C/Cl) and the image of H under the restriction map to W being Aut(W). As ire is non-trivial, this contradicts minimality of a. D. Evans, D. Macpherson, A. Ivanov 34 Finite covers with finite kernels 4 At the end of the previous section we showed how the splitting question for the finite covers of certain permutation structures reduced to the special case of superlinked covers, where the kernel is finite.

3. It says that once we know the minimal covers of W and the possible kernels, we know all the finite covers of W. For if it : C -> W is a finite cover, then Aut(C) = K. Aut(M), where M is a minimal cover of W which is an expansion of C, and K is the kernel of a. 2 Frattini covers We shall state our next result in the broader language of topological groups. So we shall say that a continuous epimorphism of Hausdorff topological groups 0 : G -> H is a Frattini cover if for every proper closed subgroup Gi of G we have O(G1) # H.

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A Canonical Form of Vector Control Systems by Korovin S. K., Il’in A. V., Fomichev V. V.

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