The Hamiltonian Circuits in Double Dihedral Group Q12 and the Symmetry Group D8

  • G. N. Shuaibu Department of Mathematics and Statistics, Faculty of Science, University of Maiduguri, P.M.B. 1069, Maiduguri, Borno State, Nigeria.
  • D. Samaila Department of Mathematics, Faculty of Science and Science Education, Adamawa State University, P.O.Box 25 Mubi, Nigeria.
Keywords: Finite groups, non-Abelian groups, Hamiltonian path, Hamiltonian circuits

Abstract

This paper analyzed all the properties of some non-Abelian finite groups with two generators, and contain only Abelian and Hamiltonian subgroups. The two exceptional groups D8 and Q12 of orders 16 and 24 respectively, were examined and are completely determined using GAP. The aim was achieved due to the fact that if a group G contains at least one Hamiltonian subgroup and if all its subgroups are either Abelian or Hamiltonian, then the group itself is Hamiltonian. We finally generate some Hamiltonian circuits in the selected groups and the possible number of circuits in each group.

Published
2019-12-20
How to Cite
Shuaibu, G. N., & Samaila, D. (2019). The Hamiltonian Circuits in Double Dihedral Group Q12 and the Symmetry Group D8. Current Research in Science and Technology Vol. 3, 125-136. Retrieved from https://stm1.bookpi.org/index.php/crst-v3/article/view/750
Issue
Current Research in Science and Technology Vol. 3
Section
Chapters