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@article{Evans:1993:10.1016/0168-0072(93)90168-D,
author = {Evans, DM and Hrushovski, E},
doi = {10.1016/0168-0072(93)90168-D},
journal = {Annals of Pure and Applied Logic},
pages = {83--112},
title = {On the automorphism groups of finite covers},
url = {http://dx.doi.org/10.1016/0168-0072(93)90168-D},
volume = {62},
year = {1993}
}

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TY  - JOUR
AB  - We are concerned with identifying by how much a finite cover of an 0-categorical structure differs from a sequence of free covers. The main results show that (in the best circumstances) this is measured by automorphism groups which are nilpotent-by-abelian. In the language of covers, these results say that every finite (regular) cover can be decomposed naturally into linked, superlinked and free covers. The superlinked covers arise from covers over a different base, and to describe this properly we introduce the notion of a quasi-cover. These results generalise results of the second author obtained in the case where the base of the cover is a grassmannian of a disintegrated set. They also give a complete proof of a statement of the second author extending this case to the case of a grassmannian of a modular set. To do this, we need to analyse the possible superlinked covers of such a set. We also give a combinatorial condition on the base of a cover which guarantees various chain conditions on finite covers over this base, and introduce a pregeometry which is useful in the analysis of finite covers with simple fibre groups. © 1993.
AU  - Evans,DM
AU  - Hrushovski,E
DO  - 10.1016/0168-0072(93)90168-D
EP  - 112
PY  - 1993///
SN  - 0168-0072
SP  - 83
TI  - On the automorphism groups of finite covers
T2  - Annals of Pure and Applied Logic
UR  - http://dx.doi.org/10.1016/0168-0072(93)90168-D
VL  - 62
ER  -

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