Recognizability of Symmetric Groups by Spectrum

被引：0
作者：
I. B. Gorshkov
机构：
[1] Sobolev Institute of Mathematics,
来源：
Algebra and Logic | 2015年 / 53卷
关键词：
finite group; simple group; symmetric group; spectrum of group; recognition by spectrum;
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学科分类号：
摘要：
The spectrum of a finite group is the set of its element orders. A finite group G is said to be recognizable by spectrum if every finite group whose spectrum coincides with the spectrum of G is isomorphic to G. It is proved the symmetric group Sn is recognizable by spectrum for n ∉ {2, 3, 4, 5, 6, 8, 10, 15, 16, 18, 21, 27, 33, 35, 39, 45}.
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页码：450 / 457
页数：7
相关论文
共 21 条
  • [1] Brandl R(1991)Finite groups whose element orders are consecutive integers J. Alg. 143 388-400
  • [2] Shi W(1994)A characterization of some alternating and symmetric groups Comm. Alg. 22 1507-1530
  • [3] Praeger CE(1997)Characterizations of finite groups by sets of orders of their elements Algebra and Logic 36 23-32
  • [4] Shi WJ(2000)A characterization of some finite groups by their element orders Alg. Coll. 7 467-476
  • [5] Mazurov VD(2002)Recognition by the set of element orders of symmetric groups of degree Sib. Math. J. 43 808-811
  • [6] Darafsheh MR(1999) and Algebra and Logic 38 159-170
  • [7] Moghaddamfar AR(2013) + 1 for prime Algebra and Logic 52 41-45
  • [8] Zavarnitsine AV(2005)Element orders in coverings of the symmetric and alternating groups Sib. Math. J. 46 396-404
  • [9] Zavarnitsine AV(2000)Recognizability of alternating groups by spectrum Algebra and Logic 39 370-377
  • [10] Mazurov VD(2015)On connection between the structure of a finite group and the properties of its prime graph J. Alg. 423 318-374
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