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

MathSciNet review:
766222

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Abstract | References | Similar Articles | Additional Information

Abstract: Infinite planar Eulerian graphs are used to show that for the covering number of the infinite simple group is two.

Here denotes the group of all permutations of a set of cardinality denotes its subgroup consisting of the permutations moving less than elements, and the covering number of a (simple) group is the smallest positive integer satisfying for every nonunit conjugacy class in .

**[**Zvi Arad, David Chillag, and Gadi Moran,**ACM**]*Groups with a small covering number*, Products of conjugacy classes in groups, Lecture Notes in Math., vol. 1112, Springer, Berlin, 1985, pp. 222–244. MR**783071**, 10.1007/BFb0072289**[**Z. Arad, J. Stavi, and M. Herzog,**AHSt**]*Powers and products of conjugacy classes in groups*, Products of conjugacy classes in groups, Lecture Notes in Math., vol. 1112, Springer, Berlin, 1985, pp. 6–51. MR**783068**, 10.1007/BFb0072286**[**Manfred Droste,**D**]*Products of conjugacy classes of the infinite symmetric groups*, Discrete Math.**47**(1983), no. 1, 35–48. MR**720606**, 10.1016/0012-365X(83)90070-5**[**Ralph H. Fox,**F**]*On Fenchel’s conjecture about 𝐹-groups*, Mat. Tidsskr. B.**1952**(1952), 61–65. MR**0053937****[**A. B. Gray,**G**]*Infinite symmetric and monomial groups*, Ph. D. Thesis, New Mexico State University, Las Cruces, 1960.**[**Xu Cheng-hao,**Hu**]*The commutators of the alternating group*, Sci. Sinica**14**(1965), 339–342. MR**0183763****[**Shimy Karni,**K**]*Covering numbers of groups of small order and sporadic groups*, Products of conjugacy classes in groups, Lecture Notes in Math., vol. 1112, Springer, Berlin, 1985, pp. 52–196. MR**783069**, 10.1007/BFb0072287**[**G. A. Miller,**Mi**]*On the Product of Two Substitutions*, Amer. J. Math.**22**(1900), no. 2, 185–190. MR**1505829**, 10.2307/2369754**[**Gadi Moran,**M**]*Parity features for classes of the infinite symmetric group*, J. Combin. Theory Ser. A**33**(1982), no. 1, 82–98. MR**665658**, 10.1016/0097-3165(82)90081-4**[**-,**M1**]*Products of conjugacy classes in some infinite simple groups*(to appear).**[**W. R. Scott,**S**]*Group theory*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR**0167513**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1985-0766222-1

Article copyright:
© Copyright 1985
American Mathematical Society