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Journal of the Ramanujan Mathematical Society

Volume 35, Issue 2, June 2020  pp. 177–189.

The Harborth constant of Dihedral groups

Authors:  Niranjan Balachandran, Eshita Mazumdar and Kevin Zhao
Author institution:Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India

Summary:  The Harborth constant of a finite group G, denoted g(G), is the smallest integer k such that the following holds: For A ⊆ G with |A| = k, there exists B ⊆ A with |B| = exp(G) such that the elements of B can be rearranged into a sequence whose product equals 1G, the identity element of G. The Harborth constant is a well studied combinatorial invariant in the case of abelian groups. In this paper, we consider a generalization g(G) of this combinatorial invariant for nonabelian groups and prove that if G is a dihedral group of order 2n with n ≥ 3, then g(G) = n + 2 if n is even and g(G) = 2n + 1 otherwise.

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