MAXIMAL SUBLATTICES AND FRATTINI SUBLATTICES OF BOUNDED LATTICES

Authors
ADAMS ME FREESE R NATION JB SCHMID J
Citation
Me. Adams et al., MAXIMAL SUBLATTICES AND FRATTINI SUBLATTICES OF BOUNDED LATTICES, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 63, 1997, pp. 110-127
Citations number
13
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
Journal title
Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics → ACNP
ISSN journal
02636115
Volume
63
Year of publication
1997
Part
1
Pages
110 - 127
Database
ISI
SICI code
0263-6115(1997)63:<110:MSAFSO>2.0.ZU;2-O
Abstract
We investigate the number and size of the maximal sublattices of a fin ite lattice. For any positive integer k, there is a finite lattice L w ith more that \L\(k) sublattices. On the other hand, there are arbitra ry large finite lattices which contain a maximal sublattice with only 14 elements. It is shown that every finite bounded lattice is isomorph ic to the Frattini sublattice (the intersection of all maximal sublatt ices) of a finite bounded lattice.