The Hamiltonian Circuits in Double Dihedral Group Q12 and the Symmetry Group D8 | Chapter 11 | Current Research in Science and Technology Vol. 3
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.
Author(s) Details
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.
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