12050

983 دكتري

دكتري

رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

هفت، [66]ص.: مصور

ص. ع. به فارسي و انگليسي

واژه نامه

1395/11/10

كتابنامه

علوم رياضي

رياضي

ID983 دكتري

Characterization of Finite Groups by Some Associated Graphs Leila Mousavi l mousavi@math iut ac ir November 23 2016 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Bijan Taeri b taeri@cc iut ac ir Advisor Dr Neda Ahanjideh ahanjideh neda@sku ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Department of Pure Mathematics University of Shahrekord Sharekord IranAbstractFor a finite group G we denote by e G the set of element orders of G Let nse G mk k e G where mk is the number of elements of order k in G In this thesis we show that PSL2 81 and PSLm 2 where m n n 1 and 2n 1 p is a prime number are uniquely determined by nse Also we definethe common divisor graph associated with G and denote by G whose vertex set is G G 1 andtwo distinct vertices x y are joined by an edge if gcd x y 1 We study the relationship betweenthe algebraic properties of groups and properties of graphs We study some parameters of G such asdiameter the number of components and the automorphism graph We show that G is planar if andonly if G 2 3 4 5 6 We study groups with regular graphs Also we determine the structure ofgroups with acyclic graphs Key Words Common divisor graph Set of the numbers of elements of the same order prime graph Mersenne number MSC 2010 20D06 20D15 20D99 05C25 05C83

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عليرضا عبدالهي، محمدرضا ودادي، غلامرضا رضايي زاده