Geodesic
On which groups can arise as the canonical group of a spherical latin bitrade
Ars mathematica contemporanea, Tome 13 (2017) no. 1, pp. 167-185 Cet article a éte moissonné depuis la source Ars Mathematica Contemporanea website

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We address a question of Cavenagh and Wanless asking: which finite abelian groups arise as the canonical group of a spherical latin bitrade? We prove the existence of an infinite family of finite abelian groups that do not arise as canonical groups of spherical latin bitrades. Using a connection between abelian sandpile groups of digraphs underlying directed Eulerian spherical embeddings, we go on to provide several, general, families of finite abelian groups that do arise as canonical groups. These families include:any abelian group in which each component of the Smith Normal Form has composite order;any abelian group with Smith Normal Form Zpn ⊕ (⨁ i = 1kZpai), where 1 ≤ k, 2 ≤ a1, a2, …, ak, p and n ≤ 1 + 2∑ i = 1k(ai − 1); andwith two exceptions and two potential exceptions any abelian group of rank two.
DOI : 10.26493/1855-3974.1141.e42
Keywords: Spherical latin bitrade, canonical group, abelian sand-pile group 
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Kyle Bonetta-Martin; Thomas A. McCourt. On which groups can arise as the canonical group of a spherical latin bitrade. Ars mathematica contemporanea, Tome 13 (2017) no. 1, pp. 167-185. doi: 10.26493/1855-3974.1141.e42

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