شبكة الزمر البوليانية المنتهية (LBG)

Authors

  • محمد الشيخ
  • رؤوف درويش

Abstract

إن الهدف من هذا العمل هو دراسة الزمرة البوليانية المنتهية والتي تعرف بأنها الزمرة التي فيها كل عنصر x رتبته 2 ، وقد أثبتنا أن رتبة الزمرة البوليانية المولدة بـ n عنصراً هي  , سنرمز للزمرة البوليانية من الرتبة   بالرمز  , كما أثبتنا أن كل زمرة بوليانية من الرتبة  ايزومورفية مع الزمرة .

وفي هذه الحالة فإن كل عنصر من عناصر الزمرة البوليانية يمكن التعبير عنه كمتتالية من n مركبة عناصرها من  , وبينّّا كذلك أن كل زمرة بوليانية هي زمرة مرتبة بعملية ترتيب   ثم إن كل زمرة بوليانية  هي شبكة مع العمليتين      إثبات أنها شبكة بوليانية .

The purpose of this paper is to study the finite Boolean group which is known as the group in which every element x has order 2. We proved that the Boolean group order was generated by n elements is  . We  refer to the Boolean group from order  as   .

In addition, we proved that every Boolean group from order  was an isomorphism with the group . So, in this situation every element of the Boolean group  can be represented as a sequence of  n projection whose elements are of . We also showed that the Boolean group is an organized group by the order operation. Thus, every Boolean is a lattice with two operations   . This proves that it is a Boolean lattice.

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Published

2018-12-09

How to Cite

1.
الشيخ م, درويش ر. شبكة الزمر البوليانية المنتهية (LBG). TUJ-BA [Internet]. 2018Dec.9 [cited 2025Apr.10];33(2). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/5227

Issue

Vol. 33 No. 2 (2011): العلوم الأساسية

Section

Articles

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