# Some combinatorial aspects of finite Hamiltonian groups

Document Type : Research Paper

Author

Faculty of Mathematics, "Al. I. Cuza" University

Abstract

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.

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### History

• Receive Date: 03 September 2011
• Revise Date: 12 June 2012
• Accept Date: 19 June 2012