Geodesic
2-Groups that factorise as products of cyclic groups, and regular embeddings of complete bipartite graphs
Ars mathematica contemporanea, Tome 6 (2013) no. 1, pp. 155-170 Cet article a éte moissonné depuis la source Ars Mathematica Contemporanea website

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We classify those 2-groups G which factorise as a product of two disjoint cyclic subgroups A and B, transposed by an automorphism of order 2. The case where G is metacyclic having been dealt with elsewhere, we show that for each e ≥ 3 there are exactly three such non-metacyclic groups G with ∣A∣ = ∣B∣ = 2e, and for e = 2 there is one. These groups appear in a classification by Berkovich and Janko of 2-groups with one non-metacyclic maximal subgroup; we enumerate these groups, give simpler presentations for them, and determine their automorphism groups.
DOI : 10.26493/1855-3974.295.270
Keywords: Regular map, complete bipartite graph, product of cyclic groups. 
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Shaofei Du; Gareth Jones; Jin Ho Kwak; Roman Nedela; Martin Škoviera. 2-Groups that factorise as products of cyclic groups, and regular embeddings of complete bipartite graphs. Ars mathematica contemporanea, Tome 6 (2013) no. 1, pp. 155-170. doi: 10.26493/1855-3974.295.270

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