Automorphism Group of Dihedral Groups With Perfect Order Subsets
Keywords:Dihedral group, Order classes, Automorphism, Conjugacy classes
AbstractLet \(G\) 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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