A note on polynomial automorphisms of finite lattices
β Scribed by H. Lakser
- Publisher
- Springer
- Year
- 1997
- Tongue
- English
- Weight
- 58 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0002-5240
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π SIMILAR VOLUMES
Schmidt proved that every distributive lattice with n join-irreducible elements can be represented as the congruence lattice of a "small" lattice I,, that is, a lattice L with O(r?) elements. G. Gratzer, I. Rival, and N. Zaguia proved that, for any o < 2, O(n\*) can not be improved to O(rF). In this
The aim of this paper is to give a characterisation of the determinants and signatures of integral ideal lattices over a given algebraic number field. This is then used to obtain an existence criterion for automorphisms of given characteristic polynomial. In particular, we give a different proof of
dedicated to professor helmut wielandt on the occasion of his 90th birthday ## 1. INTRODUCTORY REMARKS Let G be a group and denote by PAut G the group of power automorphisms of G (see [4]). An automorphism of G is called an I-automorphism of G if it maps every infinite subgroup of G onto itself. T