Arranging countably Infinite abelian groups. (English) Zbl 07921350
Summary: An interesting result due to C. St. J. A. Nash-Williams [Proc. Camb. Philos. Soc. 55, 232–238 (1959; Zbl 0089.18401)] can be used to construct enumerations of countably infinite abelian groups using sets of generators. In addition to providing a more accessible proof of this classical result, we compute, for any such group and any collection of generators, the cardinality of the set of such enumerations. These results can also be interpreted in terms of Cayley graphs for groups.
Citations:
Zbl 0089.18401References:
[1] | Nash-Williams, C.Abelian groups, graphs and generalized knights. Proc Cambridge Philos Soc. 1959;55:232-238. DOI: . · Zbl 0089.18401 |
[2] | Gallian, J.Contemporary Abstract algebra. 10th ed. Belmont, CA: Brooks/Cole; 2020. DOI: . · Zbl 1330.00006 |
[3] | Jungreis, D.Hamiltonian paths in Cayley digraphs of finitely-generated infinite abelian groups. Discrete Math. 1989;78(1-2):95-104. DOI: . · Zbl 0702.05057 |
[4] | Fuchs, L.Abelian groups. Cham: Springer; 2015. DOI: . · Zbl 1416.20001 |
[5] | Fraleigh, J.A first course in Abstract algebra. 3rd ed. Reading, MA: Addison-Wesley; 1982. DOI: . |
[6] | Corwin, S.Hamiltonicity in Cayley graphs of finite and infinite groups. Undergraduate Thesis, Whitman College; 2022. Available from: https://math.whitman.edu/SeniorProjects/2022/Sylvie/_Corwin.pdf |
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