具有较少非中心共轭类数的有限群
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摘要
给出了非中心共轭类数介于6与9之间时有限群的结构,以及非中心共轭类数为10且基柱是可解群时有限群的结构.
We classify the finite groups whose noncentral conjugacy class number is between 6 and 9 also classify the finite groups whose noncentral conjugacy class number is 10 with solvable socle.
We classify the finite groups whose noncentral conjugacy class number is between 6 and 9 also classify the finite groups whose noncentral conjugacy class number is 10 with solvable socle.
引文
[1]ANTONIO BELTRANFELIP,FELIPE MARIA JOSE,CARMEN MELCHOR BORJA.Triangles in the Graph of Conjugacy Classes of Normanl Subgroups[J].Monatshefte für Mathematik,2017,182(1):1-17.
[2]FANG Ming,ZHANG Pu.Finite Groups with Graphs Containing No Triangles[J].Journal of Algebra,2003,264(2):6 13-619.
[3]MORETOALEXANDER,QIAN Guohua,SHI Wujie.Finite Groups Whose Conjugacy Class Graphs Have Few Vertices[J].Archiv der Mathematik,2005,85(2):101-107.
[4]HUPPERT BERTRAM.Character Theory of Finite Groups[M].Berlin-New York:Walter Der Gruyter,1998.
[5]李美艳,游兴中.非中心元的共轭类较少的有限群[J].吉首大学学报(自然科学版),2014,35(4):13-16.
[6]温海风,游兴中.恰有5个非中心元的共轭类的有限群[J].吉首大学学报(自然科学版),2016,37(6):13-16.
[7]LOPEZ ANTONIO VERA,LOPEZJUAN VERA.Classification of Finite Groups According to the Number of Conjugacy Classes[J].Israel Journal of Mathematics,1985,51(4):305-338.
[8]LOPEZ ANTONIO VERA,LOPEZJUAN VERA.Classification of Finite Groups According to the Number of Conjugacy Classes II[J].Israel Journal of Mathematics,1986,56(2):188-221.
[9]LOPEZ ANTONIO VERA,SANGRONIZ JOSU.The Finite Groups with Thirteen and Fourteen Conjugacy Classes[J].Mathematische Nachrichten,2007,280(5/6):676-694.
[10]The GAP Group.GAP-Groups,Algorithms,Programming-a System for Computational Discrete Algebra[EB/OL].(2018-05-13)[2018-07-20].https:∥www.gap-system.org/.
[2]FANG Ming,ZHANG Pu.Finite Groups with Graphs Containing No Triangles[J].Journal of Algebra,2003,264(2):6 13-619.
[3]MORETOALEXANDER,QIAN Guohua,SHI Wujie.Finite Groups Whose Conjugacy Class Graphs Have Few Vertices[J].Archiv der Mathematik,2005,85(2):101-107.
[4]HUPPERT BERTRAM.Character Theory of Finite Groups[M].Berlin-New York:Walter Der Gruyter,1998.
[5]李美艳,游兴中.非中心元的共轭类较少的有限群[J].吉首大学学报(自然科学版),2014,35(4):13-16.
[6]温海风,游兴中.恰有5个非中心元的共轭类的有限群[J].吉首大学学报(自然科学版),2016,37(6):13-16.
[7]LOPEZ ANTONIO VERA,LOPEZJUAN VERA.Classification of Finite Groups According to the Number of Conjugacy Classes[J].Israel Journal of Mathematics,1985,51(4):305-338.
[8]LOPEZ ANTONIO VERA,LOPEZJUAN VERA.Classification of Finite Groups According to the Number of Conjugacy Classes II[J].Israel Journal of Mathematics,1986,56(2):188-221.
[9]LOPEZ ANTONIO VERA,SANGRONIZ JOSU.The Finite Groups with Thirteen and Fourteen Conjugacy Classes[J].Mathematische Nachrichten,2007,280(5/6):676-694.
[10]The GAP Group.GAP-Groups,Algorithms,Programming-a System for Computational Discrete Algebra[EB/OL].(2018-05-13)[2018-07-20].https:∥www.gap-system.org/.