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العنوان
Groups whose Subgroups are Smooth /
المؤلف
EL-sherif, Sara Hassan Hassan Mahmoud.
هيئة الاعداد
باحث / سارة حسن حسن
مشرف / احمد عبد القادر رمضان
مشرف / عبد المنعم محمد الخولى
الموضوع
Linear algebraic groups. group theory.
تاريخ النشر
2021.
عدد الصفحات
34 p. :
اللغة
الإنجليزية
الدرجة
ماجستير
التخصص
الجبر ونظرية الأعداد
الناشر
تاريخ الإجازة
27/6/2021
مكان الإجازة
جامعة بني سويف - كلية العلوم - الرياضيات وعلوم الحاسب
الفهرس
Only 14 pages are availabe for public view

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Abstract

A maximal chain in a finite lattice L is called smooth if any two intervals of the same length are isomorphic. A finite group G is called TS-group (totally smooth group) if all its maximal chains in its subgroup lattice are smooth, and called GS-group (generalized smooth group) if [G/N] is totally smooth for every subgroup N of G of prime order.
As a continuation to the study of smooth groups, this thesis is devoted to study some aspects of the theory of smooth groups.
In this thesis we study the structure of a finite group G if:
(1) All maximal subgroups of G are GS-groups and G has a subgroup H such that all maximal subgroups (or all minimal subgroups) of H are S-permutable in G.
(2) M{p} is a TS-set and G has a subgroup H such that every maximal subgroup of H is S-permutable in G, where M{p} is the set of all maximal subgroups of G whose orders are divided by a prime p.
Keywords:
Smooth groups, totally smooth groups, generalized smooth groups, and S-permutable subgroups.