Wilson, Andrew Philip (1985) The strong containment lattice of Schunck classes of finite soluble groups. PhD thesis, University of Warwick.

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Abstract

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.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Solvable groups
Official Date:	1985
Dates:	Date Event 1985 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Hawkes, Trevor O., 1936-
Sponsors:	Science Research Council (Great Britain)
Extent:	vii, 125 leaves
Language:	eng

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