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Transactions of the American Mathematical Society

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Of planar Eulerian graphs and permutations


Author: Gadi Moran
Journal: Trans. Amer. Math. Soc. 287 (1985), 323-341
MSC: Primary 05C25; Secondary 05C10, 05C45, 20B07, 20B22, 57M25
DOI: https://doi.org/10.1090/S0002-9947-1985-0766222-1
MathSciNet review: 766222
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Abstract: Infinite planar Eulerian graphs are used to show that for $ v > 0$ the covering number of the infinite simple group $ {H_v} = S/{S^v}$ is two.

Here $ S$ denotes the group of all permutations of a set of cardinality $ {\aleph _v},{S^v}$ denotes its subgroup consisting of the permutations moving less than $ {\aleph _v}$ elements, and the covering number of a (simple) group $ G$ is the smallest positive integer $ n$ satisfying $ {C^n} = G$ for every nonunit conjugacy class $ C$ in $ G$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0766222-1
Article copyright: © Copyright 1985 American Mathematical Society

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