%0 Journal Article %T Some combinatorial aspects of finite Hamiltonian groups %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Tarnauceanu, M. %D 2013 %\ 10/15/2013 %V 39 %N 5 %P 841-854 %! Some combinatorial aspects of finite Hamiltonian groups %K Hamiltonian groups %K Abelian groups %K automorphisms %K subgroups %K subgroup coverings %R %X In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite Hamiltonian group. %U http://bims.iranjournals.ir/article_446_709d30bd2ac8176682140ee62d6a4254.pdf