9343

8625

كارشناسي ارشد

علوم رياضي- رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

هشت،92ص.

بيژن طائري

عاطفه قرباني

دارد

17/9/93

عليرضا عبدالهي، قهرمان طاهريان

رياضي

ID8625

On groups with given same order type Leyli Jafari l jafari@math iut ac ir 2014 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Bijan Taeri b taeri@cc iut ac irAdvisor Dr Atefeh ghorbani a ghorbani@cc iut ac ir2000 MSC 20D06 20D60Keywords nilpotent groups solvable groups same order typeAbstract This M Sc thesis is based on the following papers On groups with given same order type communications in algebra 2012 40 2140 Rulin Shen 2150 Cheng K Deaconescu M Mong L L and Shi W Corrigendum and addendum to Classification of finite groups with all elements of prime order AMS 1993 117 1205 1207 Let G be a group define g h if g h G have the same order The set of sizes of the equivalence classeswith respect to this relation is called the same order type of G For instance if G 1 is torsion free its type is 1 G The only group of type 1 are 1 Z2 Note that the same order type n1 n2 nr means ni njfor i j In 1953 It introduced the concept of conjugate types Let G be a finite group and n1 n2 nr the set of integers each of wich is the index of the centralizer of some element of G in G We may assume thatn1 n2 nr 1 Then the conjugate type vector n1 n2 nr is called the conjugate typevector of G A group with the conjugate type vector n1 n2 nr is said to be a group of conjugate type n1 n2 nr Obviously a group of type 1 is only abelian It has proved that finite groups of conjugate type 1 n1 and 1 n1 n2 are nilpotent and solvable respectively Afterwards he determined finite simple groups ofconjugate type 1 n1 n2 n3 By analogy we replace the size of the conjugate class in the It s above concept tothe size of the same order elements and we can give the similar definition of a group of the same order type In this thesis we prove that a group of same order type 1 n is nilpotent and of type 1 m n is solvable Fur thermore we give the structure of these groups Let P be the class of the finite groups having all nontrivial elements of prime order Of coerse P contains thep groups of exponent p but it also contains solvable groups as A4 and even the simple group A5 Another aim ofthis thesis is to classify P groups

بيژن طائري

عاطفه قرباني

عليرضا عبدالهي، قهرمان طاهريان