# 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.

Contents
Full-Text PDF