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Automorphisms, flats and erections of pregeometries

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Roberts, Leigh Alan 1973 , 'Automorphisms, flats and erections of pregeometries', Unspecified thesis, University of Tasmania.

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Abstract

We characterize pregeometries in terms of their flats - giving
necessary and sufficient conditions for a collection of sets to be the
flats of a pregeometry.

We begin a systematic study of automorphisms of pregeometries;
arguing geometrically, we obtain the (known) factorization of a
pregeometry into component pregeometries, and express the automorphism
group of the pregeometry in terms of the automorphism groups of its
components.

We use automorphisms of pregeometries and their characterization
above by flats in the following three ways:

1. All erections of any pregeometry are constructed and their
automorphism group determined.
2. We indicate a process for obtaining all pregeometries on a
set from the geometries on smaller sets and their
automorphism groups.
3. We begin the study of the transitivity of the automorphism
group of a pregeometry on the flats and the elements of the
pregeometry.

Item Type: Thesis - Unspecified
Authors/Creators:Roberts, Leigh Alan
Keywords: Automorphisms
Copyright Holders: The Author
Copyright Information:

Copyright 1973 the author - The University is continuing to endeavour to trace the copyright
owner(s) and in the meantime this item has been reproduced here in good faith. We
would be pleased to hear from the copyright owner(s).

Additional Information:

Thesis (M.Sc.)--University of Tasmania, 1974. Bibliography: l. 83

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