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The largest higher commutator sequence

Mudrinski Nebojša

Reports on Mathematical Logic

2019

Vol. 54

83--94

Given the congruence lattice L of a finite algebra A that generates a congruence permutable variety, we look for those sequences of operations on L that have the properties of higher commutator operations of expansions of A. If we introduce the order of such sequences in the natural way the question is whether exists or not the largest one. The answer is positive. We provide a description of the largest element and as a consequence we obtain that the sequences form a complete lattice.

Commutators of diffeomorphisms of a manifold with corners

Lech J.

Demonstratio Mathematica

2007

Vol. 40, nr 2

465-480

It is shown that the identity component of the group of al compac tly suported C infinity -diffeomorphisms of a manifold with corners is perfect provided the manifold has no vertices. An analogous result for Cr -diffeomorphism still holds whenever r > n+1, wheren is the dimension of the manifold. These results constiute a generalization of a well-known theorem by Thurston and Mather on the simplicity of diffeomorphism groups of boundaryless manifolds.

Komputerowe wspomaganie nauczania z zakresu komutatorów

Strzęciwilk D.

Studia Informatica

2005

Vol. 26, nr 2

81-92

W artykule przedstawiono przykład rozwiązania systemu wspomagającego nauczanie z zakresu komutatorów. Zaprezentowano możliwości systemu dydaktycznego umożliwiającego wszechstronne ćwiczenia w ramach tematyki multiplekserów i demultiplekserów. Omówiono również możliwości systemu wspomagającego nauczanie z zakresu zagadnień komutatorów do realizacji funkcji logicznych.

The article describes an example of a solution for system aided teaching of commutators. Possibilities and versatility of exercises of didactic program used for teaching of multiplexers and demultiplexers have been presented. Possibilities of didactic system for teaching of commutators in realizations of logical functions were presented too.