Automorphism Group of Dihedral Groups With Perfect Order Subsets


  • Vinod S. Department of Mathematics, Government College for Women, Thiruvananthapuram, Kerala
  • Biju G. S. Department of Mathematics, College of Engineering, Thiruvananthapuram 695016, Kerala



Dihedral group, Order classes, Automorphism, Conjugacy classes


Let \(G\) be a finite group. The set of all possible such orders joint with the number of elements that each order referred to, is called the order classes of \(G\). The order subset of \(G\) determined by \(x\in G\) is the set of elements in \(G\) with the same order as \(x\). A group is said to have perfect order subsets (POS-group) if the cardinality of each order subset divides the group order. In this paper, we compute the order classes of the automorphism group of Dihedral group. Also, we construct a class of POS groups from the automorphism group of the Dihedral group which will serve the solution to the Perfect Order Subset Conjecture.


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How to Cite

S., V., & S., B. G. (2021). Automorphism Group of Dihedral Groups With Perfect Order Subsets. Communications in Mathematics and Applications, 12(2), 263–271.



Research Article