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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Of planar Eulerian graphs and permutations
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by Gadi Moran
Trans. Amer. Math. Soc. 287 (1985), 323-341
DOI: https://doi.org/10.1090/S0002-9947-1985-0766222-1

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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Bibliographic Information
  • © Copyright 1985 American Mathematical Society
  • 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