The cyclic decomposition of the factor group cf(Dnh×C2,Z )R(Dnh×C2) when n is an odd number
Other Title(s)
التجزئة الدائرية للزمرة الكسرية cf(Dnh×C2,Z )R(Dnh×C2) عندما n عد فردي
Joint Authors
Abbas, Husayn Hadi
al-Ghurabi, Karim Abbas Layidh
Source
Journal of Basrah Researches : Sciences
Issue
Vol. 37, Issue 4C (30 Sep. 2011), pp.206-220, 15 p.
Publisher
University of Basrah College of Education for Pure Sciences
Publication Date
2011-09-30
Country of Publication
Iraq
No. of Pages
15
Main Subjects
Abstract AR
لتكن Dn زمرة ثنائي السطوح و C2 الزمرة الدوارة ذات الرتبة 2 و Dnh زمرة الجداء المباشر للزمرتين Dn و C2(أي إن (Dnh = Dn x C2 .
لتكن cf (Dnh x C2, Z) الزمرة الابدالية لدوال الصف ذات القيم الصحيحة للزمرة Dnh x C2.
إن تقاطع cf (Dnh x C2, Z) مع زمرة كل الشواخص العمومية للزمرة Dnh x C2 و التي يرمز لها بالرمز R (Dnh X C2) تكون زمرة جزئية سوية من الزمرة cf (Dnh X C2, Z) و يرمز لها بالرمز R (Dnh X C2)، إنالزمرة الكسرية cf (Dnh X C2, Z) / R (Dnh X C2) تكون زمرة ابدالية منتهية و يرمز لها بالرمز K (Dnh X C2)..
هدف هذا البحث هو إيجاد التجزئة الدائرية لهذه الزمرة.
و قد وجد أنه عندما n عدد فردي بحيث أنه Piai mΠi=1 = n، P1, P2,…..,Pm جميعها أعداد أولية فأن : C8.
⨁I = 1 C2 ⨁I = 1 C4 2 (a1 + 1) .
(a2 + 1)…..
(am + 1) + 1 ⨁aj +1)] time] (a1 + 1) .
(a2 + 1)……..
(am + 1) + 2 πjΠj=1 m ]K (CaiPi)) Σ ⨁i=1( mΣ ⨁] i=1 ⨁K(Dnhx C2) = 4
Abstract EN
Let Dn be the dihedral group, C2 be the cyclic group of order 2 and Dnh is the direct product group of Dn and C2 i.e.(Dnh=Dn×C2).
Let cf (Dnh×C2,Z) be the abelian group of Zvalued class functions of the group Dnh×C2 .
The intersection cf (Dnh×C2,Z) with the group of all generalized characters of Dnh×C2 which is denoted by R (Dnh×C2), is a normal subgroup of cf (Dnh×C2,Z) denoted by R (Dnh×C2), then factor group cf (Dnh×C2,Z)/R (Dnh×C2) is a finite abelian group denoted by K(Dnh×C2.
T he problem of determining the cyclic decomposition of the group K(Dnh×C2) seem to be untouched .
The aim of this paper is to find the cyclic decomposition of this group.
We find that when n is an odd number such that, n = Π P α ,where all pi 's are distinct primes.
American Psychological Association (APA)
Abbas, Husayn Hadi& al-Ghurabi, Karim Abbas Layidh. 2011. The cyclic decomposition of the factor group cf(Dnh×C2,Z )R(Dnh×C2) when n is an odd number. Journal of Basrah Researches : Sciences،Vol. 37, no. 4C, pp.206-220.
https://search.emarefa.net/detail/BIM-286188
Modern Language Association (MLA)
Abbas, Husayn Hadi& al-Ghurabi, Karim Abbas Layidh. The cyclic decomposition of the factor group cf(Dnh×C2,Z )R(Dnh×C2) when n is an odd number. Journal of Basrah Researches : Sciences Vol. 37, no. 4C (Sep. 2011), pp.206-220.
https://search.emarefa.net/detail/BIM-286188
American Medical Association (AMA)
Abbas, Husayn Hadi& al-Ghurabi, Karim Abbas Layidh. The cyclic decomposition of the factor group cf(Dnh×C2,Z )R(Dnh×C2) when n is an odd number. Journal of Basrah Researches : Sciences. 2011. Vol. 37, no. 4C, pp.206-220.
https://search.emarefa.net/detail/BIM-286188
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 219
Record ID
BIM-286188
