Polygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1)
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Polygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1)
Polygroup Theory and Related Systems\\b World ScientificPolygroup Theory and Related SystemsThis page intentionally left blankPolygroup Theory and Rel Polygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1) lated SystemsBijan DavvazYazd University, IranWorld ScientificPublished byWorld Scientific Publishing Co. Pie. Lid.5 Toh Tuck Link. Singapore 596224USA office: 27 Warren Street. Suite 401-402. Hackensack. NJ 07601UK office: 57 Shelton Street, Covent Garden. London WC2H 9HEBritish Library Cataloguing Polygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1) -in-Publication DataA catalogue record for this book is available from the British Library.POLYGROUP THEORY’ AND RELATED SYSTEMSCopyright © 2013 by WoPolygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1)
rld Scientific Publishing Co. Pte. Ltd.All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronicPolygroup Theory and Related Systems\\b World ScientificPolygroup Theory and Related SystemsThis page intentionally left blankPolygroup Theory and Rel Polygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1) ion from the Publisher.For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc.. 222 Rosewood Drive, Danvers. MA 01923. USA. In this case permission to photocopy is not required from the publisher.ISBN 978-981-4425-30-8Printed in Singapore.Pr Polygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1) efaceThe theory of groups is the oldest branch of ordinary algebra. The concept of a hypergroup which is a generalization of the concept of a group, fPolygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1)
irst was introduced by Marty. Indeed, hypergroups represent a natural extension of groups. In a group, the composition of two elements is an element, Polygroup Theory and Related Systems\\b World ScientificPolygroup Theory and Related SystemsThis page intentionally left blankPolygroup Theory and Rel Polygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1) olygroups which arc certain subclass of hypergroups are used to study color algebra and combinatorics.The idea to write this book, and more important the desire to do so. is a direct outgrowth of a course 1 gave in the department of mathematics at Yazd University. One of my main aims was to present Polygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1) an introduction to this recent progress in the theory of polygroups and related systems. I have tried to keep the preliminaries down to a bare minimumPolygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1)
. The book covers most of the mathematical ideas and techniques required in the study of poly groups.The presented book is composed by five chapters. Polygroup Theory and Related Systems\\b World ScientificPolygroup Theory and Related SystemsThis page intentionally left blankPolygroup Theory and Rel Polygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1) heir history and some basic results on some important classes of hypergroups such as complete hypergroups, join spaces and canonical hypergroups. The following chapters arc about polygroups. In third chapter, the concept of polygroups and some examples arc presented. Then, fundamental relations defi Polygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1) ned on polygroups, isomorphism theorems, permutation polygroups, polygroup hyperrings, solvable polygroiqxs and nilpotent polygroups are studied. ThePolygroup-Theory-and-Related-System-by-Bijaan-Davvaz(1)
fourth chapter deal with the concepts of weak algebraic hyperstructures: and the notions of F/v-groups (weak hypergroups) and weak polygroups an' studPolygroup Theory and Related Systems\\b World ScientificPolygroup Theory and Related SystemsThis page intentionally left blankPolygroup Theory and RelPolygroup Theory and Related Systems\\b World ScientificPolygroup Theory and Related SystemsThis page intentionally left blankPolygroup Theory and RelGọi ngay
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