Cover-avoidance properties and the structure of finite groups

AbstractWe call a subgroup A of a finite group G a CAP-subgroup of G if for any chief factor H/K of G, we have H∩A=K∩A or HA=KA. In this paper, some characterizations for a finite group to be solvable are obtained under the assumption that some of its maximal subgroups or 2-maximal subgroups be CAP-subgroups. We also determine the p-solvability and p-nilpotency of finite groups by considering their CAP-subgroups

Completion of codes with finite bi-decoding delays

AbstractLet A∗ be a free monoid generated by a set A and let X⊆A∗ be a code with property P. The embedding of X into a complete code Y⊆A∗ with the same property P is called the completion of X. The method of completion of rational bifix codes and codes with finite decoding delays have been investigated by a number of authors. In this paper, we provide a general method of construction for completing the codes with finite bi-decoding delays. As a consequence, the completion method of rational bifix codes and codes with finite decoding delays is extended and applied to codes with finite bi-decoding delays

Representations of strongly algebraically closed algebras

We introduce the notion of q′-compactness for MV-algebras. One of the main results of the paper is a characterization of a class of orthomodular lattices that are horizontal sums of strongly algebraically closed algebras

Baer semisimple modules and Baer rings

We consider Baer rings and Baer semisimple R-modules which are generalizations of semisimple modules. Several characterization theorems of Baer semisimple modules are obtained. In particular, we prove that a ring R is a Baer ring if and only if R itself, regarded as a regular R-module, is Baer semisimple

Retract extensions of ordered sets

The concept of retract extension of an ordered set is introduced and studied. We give an example of a retract extension and an example that is not a retract extension. Bibliography: 12 titles. ©2006 Springer Science+Business Media, Inc

III-Homomorphisms and III-congruences on posets

A new homomorphism between two partially ordered sets (the III-homomorphism) and a new congruence on a poset (the III-congruence) are introduced. Some properties of these homomorphisms and congruences and their relationship to the other known homomorphisms and congruences on posets are investigated. In contrast to total algebras, there are many different ways to introduce these notions. It is usually required that the respective notions should coincide with the usual definitions whenever lattices or semilattices are treated. The present paper presents an approach which in some sense completes the hierarchy of definitions so far used. © 2007 Elsevier B.V. All rights reserved