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Article
On Representation of Monomial Groups

Authors: S.A.Bedai --- A.A.Hajim
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2011 Volume: 14 Issue: 3 Pages: 135-138
Publisher: Al-Nahrain University جامعة النهرين

Abstract

Taketa shows that all monomial groups (commonly written as M-groups) are solvable. Gajendragadkar gives the notion of π-factorable character. We show that an irreducible character of an M-group is primitive if it is π-factorable. Issacs proves that product of two monomial characters is a monomial. We extend this fact to include any finite number of monomial characters consequently we prove that any product of finite number of M-groups is an M-group. We show that any group of order 45 is an M-group and for any group G, the factor group is an M-group.

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Article
REPRESENTATION OF GROUPS BY HOMOMORPHISM
تمثيل الزمر بواسطة التشاكلات

Author: S.A.Bedaiwi سعد عويد بديوي
Journal: Iraqi Journal of Science المجلة العراقية للعلوم ISSN: 00672904/23121637 Year: 2012 Volume: 53 Issue: 3 Pages: 629-632

Abstract

Issacs [1] shows that if is a homomorphism ( is the multiplicative group of the field F) and is a group, then one can define which is an F-representation of of degree 1 affords as character. [2,3,4] inspires us to do the following: given a homomorphism then we define a representation of by the homomorphism from a given F-representation of as . We study this kind of representations and their associated characters.

Isaacs [1] بين بانه اذا كان تشاكل ( هي زمرة الضرب للحقل F و زمرة ما), فانه من الممكن تعريف وهو تمثيل F ل من الدرجة 1 وله كشاخص . المصادر [2,3,4]الهمتنا لفعل ما يلي: ليكن تشاكل زمري , نعرف تمثيل ل بواسطة التشاكل من التمثيل F ل بالشكل , ندرس هذه الانواع من التمثيلات مع شواخصها.

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Article
On the Representations of M-Groups
M حول تمثيلات الزمر -

Authors: Taghreed Hur Majeed --- Khawla A.Al-Zubaidy --- Niran Sabah Jasim
Journal: Baghdad Science Journal مجلة بغداد للعلوم ISSN: 20788665 24117986 Year: 2016 Volume: 13 Issue: 2 Pages: 394-401

Abstract

The main object of this paper is to study the representations of monomial groups and characters technique for representations of monomial groups. We refer to monomial groups by M-groups. Moreover we investigate the relation of monomial groups and solvable groups. Many applications have been given the symbol G e.g. group of order 297 is an M-group and solvable. For any group G, the factor group G/G (G is the derived subgroup of G) is an M-group in particular if G = Sn, SL(4,R).

الهدف الرئيسي من البحث هو دراسة حول تمثيلات الزمر الاحادية وتقنية المميزات (الشواخص) في تمثيلات الزمر الاحادية. رمزنا للزمر الاحادية بالزمرM-. ثم بحثنا العلاقة بين الزمر الاحادية والزمر القابلة للحل. أعطينا عدد من التطبيقات مثلا ً اي زمرة من الرتبة 297 تكون زمرة احادية وقابلة للحل لأي زمرة G تكون زمرة القسمة G/G زمرة احادية كحالة خاصة G = Sn, SL(4,R).

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