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Some lattice properties of normal-by-finite subgroups

Maria De Falco, Carmela Musella (2003)

Bollettino dell'Unione Matematica Italiana

A subgroup H of a group G is said to be normal-by-finite if the core H G of H in G has finite index in H . It has been proved by Buckley, Lennox, Neumann, Smith and Wiegold that if every subgroup of a group G is normal-by-finite, then G is abelian-by-finite, provided that all its periodic homomorphic images are locally finite. The aim of this article is to describe the structure of groups G for which the partially ordered set nf G consisting of all normal-by-finite subgroups satisfies certain relevant...

Some problems in number theory that arise from group theory.

Alexander Moretó (2007)

Publicacions Matemàtiques

In this expository paper, we present several open problerns in number theory that have arisen while doing research in group theory. These problems are on arithmetical functions or partitions. Solving some of these problems would allow to solve some open problem in group theory.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].

Some properties of B -operations

Bohdan Butkiewicz (2007)

Kybernetika

In the paper the problem of mathematical properties of B -operations and weak W B -operations introduced by the author for interpretation of connectives “and”, “or”, and “also” in fuzzy rules is considered. In previous author’s papers some interesting properties of fuzzy systems with these operations were shown. These operations are weaker than triangular norms used commonly for a fuzzy system described by set of rules of the type if – then. Monotonicity condition, required for triangular norms, is...

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