The Number of Group Homomorphisms from $D_m$ into $D_n$
Abstract
Counting homomorphisms between cyclic groups is a common exercise in a first course in abstract algebra. A similar problem, accessible at the same level, is to count the number of group homomorphisms from a dihedral group of order $2m$ into a dihedral group of order $2n$. While the solution requires only elementary group theory, the result does not appear in the literature or in the usual texts. As the solution may be of interest, particularly to those teaching undergraduate abstract algebra, it is provided in this note.
 Publication:

arXiv eprints
 Pub Date:
 January 2012
 arXiv:
 arXiv:1201.2363
 Bibcode:
 2012arXiv1201.2363J
 Keywords:

 Mathematics  Group Theory;
 20D99
 EPrint:
 The College Mathematics Journal, vol. 44 no. 3, pp. 190192, 2013