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arXiv · 1112.2376

2-Groups that factorise as products of cyclic groups, and regular embeddings of complete bipartite graphs

Shaofei Du·Gareth Jones·Jin Ho Kwak·Roman Nedela·Martin Skoviera
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Abstract

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>2 there are exactly three such non-metacyclic groups G with $|A|=|B|=2^e$, 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.

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Shaofei Du, Gareth Jones, Jin Ho Kwak, Roman Nedela, Martin Skoviera. 2011-12-11. 2-Groups that factorise as products of cyclic groups, and regular embeddings of complete bipartite graphs. https://arxiv.org/abs/1112.2376

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