| On Finite Groups with Special Conjugacy Classes |
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| 作者姓名： | 杜祥林 |
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| 作者单位： | Department of |
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| 基金项目： | The Natural Science Foundation of Chongqing Education Committee （ No. KG051107） |
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| 摘 要： | IntroductionIn 1973, Markel1]began to investigate the“S3-conjecture”; that is,S3is the only finite group inwhich every conjugacy class has different order(note: the“order”here from Ref.2] means thelength of a conjugacy class of a group). Many schol-…
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| 关 键 词： | 有限群 共轭类阶 高阶 可解群 |
| 文章编号： | 1005-2429（2007）02-0172-03 |
| 收稿时间： | 2006-04-13 |
On Finite Groups with Special Conjugacy Classes |
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| DU Xiang-lin.On Finite Groups with Special Conjugacy Classes[J].Journal of Southwest Jiaotong University,2007,15(2):172-174. |
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| Authors: | DU Xiang-lin |
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| Abstract: | Let G be a finite group with the property that for any conjugacy class order, G has exactly two conjugacy classes which have the same order. We prove that(1) if a Sylow 2-subgroup of G is Abelian, then G is isomorphic to the direct product of symmetric group with order 3 and cyclic group with order 2, or G is isomorphic to the semidirect product of a cyclic group with order 3 and a cyclic group with order 4; (2) if G' is nilpotent, then G is a group of {2,3,5}. |
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| Keywords: | Solvable groups Conjugacy class Conjugacy class order |
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