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Title: The strong containment lattice of Schunck classes of finite soluble groups
Author: Wilson, Andrew Philip
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1985
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This thesis is an investigation into some of the lattice properties of the strong containment lattice (H, «) of Schunck classes and also of its important sublattice (D, «). The general aim is to characterise lattice properties of Schunck classes by avoidance class properties. Our main result, Theorem 8.5, is an avoidance class characterisation of those D-classes all of whose maximal ascending proper chains of Q-classes to S have the,same length. The problem extended to H is much more difficult but in Corollary 4.3 we describe an avoidance class condition for a Schunck class only to have chains of finite length to S. The lack of duality in H shows up clearly in section 3. The fascinating problem of deciding whether or not H is atomic is considered in section 9. Our results suggest that it probably is since any counterexample must be very complicated.
Supervisor: Not available Sponsor: Science Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics Mathematics