Geodesic
On the number of group homomorphisms between certain groups
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 277-285.

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Let H be a finite abelian group and Dih(H) = 〈 H, b | b^2 = 1 amp; bhb^-1 = h^-1; ∀ h ∈ H 〉 be the generalized dihedral group of H. The aim of this paper is to compute the number of group homomorphisms between two generalized dihedral groups and a generalized dihedral group and an abelian group. One of these results generalized an earlier work by J. W. Johnson published in 2013.
Keywords: group homomorphism, generalized dihedral group, abelian group 
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Ashrafi, Ali Reza; Jahangiri, Bardia; Yousefian-Arani, Mohammad Moein. On the number of group homomorphisms between certain groups. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 277-285. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a2/

[1] M. Bate, The number of homomorphisms from finite groups to classical groups, J. Algebra 308 (2007) 612–628. https://doi.org/10.1016/j.jalgebra.2006.09.003

[2] N. Chigira and Y. Takegahara, On the number of homomorphisms from a finite group to a general linear group, J. Algebra 232 (2000) 236–254. https://doi.org/10.1006/jabr.1999.8398

[3] J.A. Gallian and J. Van Buskirk, The number of homomorphisms from Zm into Zn, Amer. Math. Monthly 91 (1984) 196–197. https://doi.org/10.2307/2322360

[4] J.W. Johnson, The number of group homomorphisms from Dm into Dn, College Math. J. 44 (2013) 190–192. https://doi.org/10.4169/college.math.j.44.3.190

[5] H. Katsurada, Y. Takegahara and T. Yoshida, The number of homomorphisms from a finite abelian group to a symmetric group, Comm. Algebra 28 (2000) 2271–2290. https://doi.org/10.1080/00927870008826958

[6] M. Liebeck and A. Shalev, The number of homomorphisms from a finite group to a general linear group, Comm. Algebra 32 (2004) 657–661. https://doi.org/10.1081/AGB-120027921

[7] D. Matei and A. Suciu, Counting homomorphisms onto finite solvable groups, J. Algebra 286 (2005) 161–186. https://doi.org/10.1016/j.jalgebra.2005.01.009

[8] D.J. Robinson, A Course in the Theory of Groups (Springer-Verlag, New York, 1996). https://doi.org/10.1007/978-1-4419-8594-1

[9] Y. Takegahara, The number of homomorphisms from a finite abelian group to a symmetric group (II)}, Comm. Algebra 44 (2016) 2402–2442. https://doi.org/10.1080/00927872.2015.1053896

[10] Y. Takegahara, A generating function for the number of homomorphisms from a finitely generated Abelian group to an alternating group, J. Algebra 248 (2002) 554–574. https://doi.org/10.1006/jabr.2000.8666

[11] The GAP Team, Group, GAP – Groups, Algorithms, and Programming (Version 4.5.5, 2012), http://www.gap-system.org.

[12] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (North-Holland, New York-Amsterdam-Oxford, 1982).

[13] G. Chartrand, F. Harary and P. Zhang, On the geodetic number of a graph, Networks 39 (2002) 1–6.