دفاعیه دکتری در دانشکده ریاضی و علوم کامپیوتر
مرتضی العلاق (دانشجوی بین‌المللی دوره دکتری دانشکده ریاضی و علوم کامپیوتر-گرایش جبر)، ۱۲ مهرماه ۱۴۰۲ از رساله دکتری خود با عنوان «حرکت گروه‌های جایگشتی» دفاع کرد.
چکیده این رساله که به راهنمایی دکتر مهدی علائیان انجام شده، به شرح زیر است:
چکیده:
Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer. Let Γ⊆Ω. If for each g∈G the size |Γ^gΓ| is bounded, we define the movement of Γ as move(Γ)= max_(g∈G ) |Γ^g-Γ|. If move(Γ) ≤m for all Γ⊆Ω, then G is said to have bounded movement and the movement of G is defined as the maximum of move(g) over all non-identity elements of g∈G. Similarly, for each ۱≠g∈G, we define the movement of g as max|Γ^gΓ| over all subsets Γ of Ω.
Therefore, in this thesis we will classify all transitive permutation groups with movement m with maximum bound, or each element has movement with some conditions. In particular, we will investigate all transitive permutation groups G with bounded movement equal to m such that G is not a ۲-group but in which every non-identity element has the movement m or m-۱, every non-identity element has the movement m or m-۲, and every non-identity element of movement three consecutive integers.
کلمات کلیدی:
Permutation group, Transitive, Bounded movement, Fixed point free
Element
نشانی الکترونیکی دانشجو: murtadha.alallaq gmail.com |
