Archivo por meses: mayo 2014

Paper «A description based on languages of the final non-deterministic automaton» published in Theoret. Comput. Sci.

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A. Ballester-Bolinches, E. Cosme-Llópez, R. Esteban-Romero

A description based on languages of the final non-deterministic automaton

Theoret. Comput. Sci., 536 (2014), 1–20

http://dx.doi.org/10.1016/j.tcs.2014.01.018

Abstract

The study of the behaviour of non-deterministic automata has traditionally focused on the languages which can be associated to the different states. Under this interpretation, the different branches that can be taken at every step are ignored. However, we can also take into account the different decisions which can be made at every state, that is, the branches that can be taken, and these decisions might change the possible future behaviour. In this case, the behaviour of the automata can be described with the help of the concept of bisimilarity. This is the kind of description that is usually obtained when the automata are regarded as labelled transition systems or coalgebras.

Contrarily to what happens with deterministic automata, it is not possible to describe the behaviour up to bisimilarity of states of a non-deterministic automaton by considering just the languages associated to them. In this paper we present a description of a final object for the category of non-deterministic automata, regarded as labelled transition systems, with the help of some structures defined in terms of languages. As a consequence, we obtain a characterisation of bisimilarity of states of automata in terms of languages and a method to minimise non-deterministic automata with respect to bisimilarity of states. This confirms that languages can be considered as the natural objects to describe the behaviour of automata.

Keywords: Non-deterministic automaton; Formal language; Coalgebra; Bisimilarity; Final automaton

Visita y charla del profesor Gil Kaplan

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El profesor Gil Kaplan, de la School of Computer Science del Academic College of Tel Aviv-Yafo (Israel), visitará el Departament d’Àlgebra de la Universitat de València entre los días 26 y 29 de mayo de 2014. El profesor Kaplan es especialista en teoría abstracta de grupos finitos.

El martes 27 de mayo, a las 11.30, impartirá la charla titulada

Nilpotency, solvability and the twisting function of finite groups

en el seminario del Departament d’Àlgebra de la Universitat de València (segundo piso de la Facultat de Matemàtiques). Estáis todos invitados.

 

Paper “Primitive subgroups and PST-groups” published in Bull. Aust. Math. Soc

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The following paper has been published:

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El següent article ha sigut publicat:

A. Ballester-Bolinches, J. C. Beidleman, R. Esteban-Romero

Primitive groups and PST-groups

Bull. Aust. Math. Soc., 89 (2014), 373–378

http://dx.doi.org/10.1017/S0004972713000592

Abstract

All groups considered in this paper are finite. A subgroup H of a group G is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of G containing H as a proper subgroup. He et al. [‘A note on primitive subgroups of finite groups’, Commun. Korean Math. Soc. 28(1) (2013), 55–62] proved that every primitive subgroup of G has index a power of a prime if and only if G/Φ(G) is a solvable PST-group. Let X denote the class of groups G all of whose primitive subgroups have prime power index. It is established here that a group G is a solvable PST-group if and only if every subgroup of G is an X-group.

2010 Mathematics subject classification: primary 20D10; secondary 20D15, 20D20

Keywords and phrases: finite groups, primitive subgroups, solvable PST-groups, T0-groups

Paper «On a class of supersoluble groups» accepted for publication in Bull. Aust. Math. Soc.

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The following paper has been accepted for publication.

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El següent article ha sigut acceptat per ser publicat.

A. Ballester-Bolinches, J. C. Beidleman, R. Esteban-Romero, M. F. Ragland

On a class of supersoluble groups

Bull. Aust. Math. Soc., in press

http://dx.doi.org/10.1017/S0004972714000306

We will inform about the publication details.

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Abstract: A subgroup H of a finite group G is said to be S-permutable in G if H permutes with every Sylow q-subgroup of G for all primes q not dividing |H|. A finite group G is an MS-group if the maximal subgroups of all the Sylow subgroups of G are S-semipermutable in G. The aim of the present paper is to characterise the finite MS-groups.
2010 Mathematics subject classification: 20D10, 20D15, 20D20

Keywords: Finite group, soluble PST-group, T_0-group, MS-group, BT-group.

Paper «Some subgroup embeddings in finite groups» accepted for publication in J. Adv. Res.

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The following paper has been accepted for publication.

El siguiente artículo ha sido aceptado para su publicación.

El següent article ha sigut acceptat per ser publicat.

A. Ballester-Bolinches, J. C. Beidleman, R. Esteban-Romero, M. F. Ragland

Some subgroup embeddings in finite groups

J. Adv. Res., in press

http://dx.doi.org/10.1016/j.jare.2014.04.004

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Abstract: In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied.

2010 Mathematics subject classification:

20D05, 20D10, 20F16

Keywords: Finite group; Permutability; S-permutability; Semipermutability; Primitive subgroup; Quasipermutable subgroup.