| Characterizability of the Group ^2Dp（3） by its Order Components,Where p ≥ 5 is a Prime Number Not of the Form 2^m ＋ 1 |
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| 作者姓名： | M. R. DARAFSHEH |
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| 作者单位： | School of Mathematics, College of Science, University of Tehran, Tehran, Iran |
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| 基金项目： | Acknowledgements This research was done at the Mathematics Department of the University of North Carolina at Charlotte, USA, while the author had a visiting position in 2006-2007. The author deeply appreciates the kindness and hospitality of the chair and the cochair of the UNCC Mathematics Department. The support of the University of Tehran is also acknowledged. |
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| 摘 要： | The author will prove that the group ^2Dp（3） can be uniquely determined by its order components, where p ≠ 2^m ＋ 1 is a prime number, p ≥ 5. More precisely, if OC（G） denotes the set of order components of G, we will prove OC（G） = OC（^2Dp（3）） if and only if G is isomorphic to ^2Dp（3）. A main consequence of our result is the validity of Thompson＇s conjecture for the groups under consideration.
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| 关 键 词： | 素数 图表 次数成分 线性群 |
Characterizability of the group 2Dp(3) by its order components, where p ≥ 5 is a prime number not of the form 2m + 1 |
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| M. R. DARAFSHEH.Characterizability of the group 2Dp(3) by its order components, where p ≥ 5 is a prime number not of the form 2m + 1[J].Acta Mathematica Sinica,2008,24(7):1117-1126. |
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| Authors: | M R Darafsheh |
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| Institution: | (1) School of Mathematics, College of Science, University of Tehran, Tehran, Iran |
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| Abstract: | The author will prove that the group 2
D
p
(3) can be uniquely determined by its order components, where p ≠ 2
m
+ 1 is a prime number, p ≥ 5. More precisely, if OC(G) denotes the set of order components of G, we will prove OC(G) = OC(2
D
p
(3)) if and only if G is isomorphic to 2
D
p
(3). A main consequence of our result is the validity of Thompson’s conjecture for the groups under consideration.
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| Keywords: | prime graph order component linear group |
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