Dihedral groups - Open Access .click

Creative Mathematics and Informatics, 2023
The automorphism group of a Dihedral group of order 2n is isomorphic to the holomorph of a cyclic group of order n. The holomorph of a cyclic group of order n is a complete group when n is odd. Hence automorphism groups of Dihedral groups of order 2n are its own automorphism groups whenever n is odd. In this paper, we prove that the result is also true
Sajikumar, Sadanandan +2 more
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Nilpotent Covers of Dihedral Groups

Ars Combinatoria
Let G be a group, and let c ∈ Z + ∪ { ∞ } . We let σ c ( G ) be the maximal size of a subset X of G such that, for any distinct x 1 , x 2 ∈ X , the group ⟨ x 1 , x 2 ⟩ is not c -nilpotent; similarly we let Σ c ( G ) be the smallest number of c -nilpotent subgroups of G whose union is equal to G .
Kimeu Arphaxad Ngwava, Nick Gill
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Difference sets in dihedral groups

Designs, Codes and Cryptography, 1991
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Leung, K.H., Ma, S.L., Wong, Y.L.
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Hadamard Matrices and Dihedral Groups

Designs, Codes and Cryptography, 1996
An \(n\times n\) matrix with elements \(0\) and \(1\) is called an Hadamard matrix, if the matrix \(H\) obtained from it by changing \(0\)'s to \(-1\)'s satisfies \(HH'=nI_n\). Let \(\text{D}_{2p}\) be a dihedral group of order \(2p\), where \(p\) is an odd integer and \(\mathbb{Z}\text{D}_{2p}\) be the group ring of \(\text{D}_{2p}\) over the ring ...
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