Completing partial transversals of Cayley tables of Abelian groups

Authors

Jaromy Kuhl
Donald McGinn
Michael W. Schroeder, Marshall UniversityFollow

Document Type

Article

Publication Date

9-2021

Abstract

In 2003 Grüttmüller proved that if n ⩾ 3 is odd, then a partial transversal of the Cayley table of ℤₙ with length 2 is completable to a transversal. Additionally, he conjectured that a partial transversal of the Cayley table of ℤₙ with length k is completable to a transversal if and only if n is odd and either n ∈ {k, k + 1} or n ⩾ 3k - 1. Cavenagh, Hämäläinen, and Nelson (in 2009) showed the conjecture is true when k = 3 and n is prime. In this paper, we prove Grüttmüller's conjecture for k = 2 and k = 3 by establishing a more general result for Cayley tables of Abelian groups of odd order.

Comments

The copy of record is available from the publisher at https://doi.org/10.37236/9386. Copyright © The authors. Released under the CC BY-ND license (International 4.0).

Recommended Citation

Kuhl J, McGinn D, Schroeder MW. Completing partial transversals of Cayley tables of Abelian groups. The Electronic Journal of Combinatorics. 2021 Sep 24:P3-60.