## Finite Covers With Finite Kernels (1995)

Venue: | Ann. Pure Appl. Logic |

Citations: | 4 - 4 self |

### BibTeX

@ARTICLE{Evans95finitecovers,

author = {David M. Evans},

title = {Finite Covers With Finite Kernels},

journal = {Ann. Pure Appl. Logic},

year = {1995}

}

### OpenURL

### Abstract

We are concerned with the following problem. Suppose \Gamma and \Sigma are closed permutation groups on infinite sets C and W and ae : \Gamma \Gamma! \Sigma is a non-split, continuous epimorphism with finite kernel. Describe (for fixed \Sigma) the possibilities for ae. Here, we consider the case where ae arises from a finite cover ß : C \Gamma! W . We give reasonably general conditions on the permutation structure hW ; \Sigmai which allow us to prove that these covers arise in two possible ways. The first way, reminiscent of covers of topological spaces, is as a covering of some \Sigma-invariant digraph on W . The second construction is less easy to describe, but produces the most familiar of these types of covers: a vector space covering its projective space. AMS classification: 03C35 and 20B27. 0 Introduction Various natural model-theoretic questions can be cast into the following form: Given a structure, what additional structure can be put on one part of it without affecting the s...

### Citations

538 | Model theory
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262 |
Endliche Gruppen I
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72 |
Algebraic topology
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11 |
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5 |
Invariant subspaces of V
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5 |
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4 |
Splittings of finite covers of @ 0 -categorical structures
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The structure of totally categorical structures', In: Automorphisms of First-Order Structures
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and Ehud Hrushovski, `On the automorphism groups of finite covers
- Evans
- 1993
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Citation Context ...mmas on finite covers, and then review the material we need from [4] on coverings of digraphs. 1.1 Finite covers The first part of the following lemma (which, for countable C, is essentially (1.2) of =-=[5]-=-) shows that the condition in (1ii) of Definition 0.3 that ae has image Aut(W ) can be weakened to the image of ae being dense in Aut(W ). Lemma 1.1 (i) Suppose C is a countable permutation structure ... |