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1. A note on $p$-nilpotency of finite groups | |||
HUO Li-Jun,MAHBOOB Abid,GUO Wen-Bin | |||
Mathematics 23 October 2013 | |||
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Abstract:In this paper, the structure of a finite group $G$ under the assumption thatthe maximal subgroups of a Sylow subgroup is eithersemi cover-avoiding or $S$-quasinormally embedded subgroups in $G$ are studied.Some new characterizations on the $p$-nilpotency of finite groups are obtained, and some known results are generalized. | |||
TO cite this article:HUO Li-Jun,MAHBOOB Abid,GUO Wen-Bin. A note on $p$-nilpotency of finite groups[OL].[23 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4565445 |
2. Alternating groups and flag-transitive $2-(v,k,4)$ symmetric designs | |||
DONG Huili,ZHOU Shenglin | |||
Mathematics 26 December 2011 | |||
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Abstract:In this paper, we study the classification offlag-transitive, point-primitive 2-(v,k,4) symmetric designs. Weprove that if the socle of the automorphism group of aflag-transitive, point-primitive nontrivial2-(v,k,4) symmetric design D is an alternating group An for n>=5, then (v,k)=(15,8) and D=(P,B) is one of the following:(i) P is the set of one-dimensional subspaces of V4(2), B is acollection of PX, where X is the set of one-dimensional subspacescontained in one hyperplane of V4(2), G=A7 or A8, andthe stabiliser Gx=L3(2) or AGL3(2) respectively.(ii) P is the set of 2- of Ω6: ={1,2,..., 6}, B is a collection ofPX, where X is Y{Y}U{Z is a 2- of Ω6 Z∩Y=θ}, Y is a 2- of Ω6, G=A6 or S6, and Gx=S4 or S4*Z2 respectively. | |||
TO cite this article:DONG Huili,ZHOU Shenglin. Alternating groups and flag-transitive $2-(v,k,4)$ symmetric designs[OL].[26 December 2011] http://en.paper.edu.cn/en_releasepaper/content/4457833 |
3. A note on cover-avoiding properties of finite groups | |||
Liu Jianjun,Guo Xiuyun | |||
Mathematics 29 November 2010 | |||
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Abstract:A subgroup H of a group G is said to be a CAP*-subgroup of a group G if, for any non-Frattini chief factor K/L of G, we have HK=HL or H∩K=H∩L. In this paper, some new characterizations for finite groups are obtained based on the assumption that some subgroups are CAP*-subgroups of G. | |||
TO cite this article:Liu Jianjun,Guo Xiuyun. A note on cover-avoiding properties of finite groups[OL].[29 November 2010] http://en.paper.edu.cn/en_releasepaper/content/4393884 |
4. The influence of CAP*-subgroups on the solvability of finite groups | |||
Liu Jianjun ,Guo Xiuyun ,Li Shirong | |||
Mathematics 02 April 2010 | |||
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Abstract:A subgroup H of a group G is said to be a CAP*-subgroup of a group G if, for any non-Frattini chief factor K/L of G, we have HK=HL or H∩K=H∩L. In this paper, some new characterizations for finite solvable groups are obtained based on the assumption that some subgroups are CAP*-subgroups of G. | |||
TO cite this article:Liu Jianjun ,Guo Xiuyun ,Li Shirong. The influence of CAP*-subgroups on the solvability of finite groups[OL].[ 2 April 2010] http://en.paper.edu.cn/en_releasepaper/content/41494 |
5. A counter-example to a conjecture of Lusztig | |||
Shi Jianyi | |||
Mathematics 12 January 2010 | |||
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Abstract:Lusztig defined two functions a and a\ | |||
TO cite this article:Shi Jianyi. A counter-example to a conjecture of Lusztig[OL].[12 January 2010] http://en.paper.edu.cn/en_releasepaper/content/38811 |
6. Quasirecognition by prime graph of the simple group $ E_7(q)$ | |||
Zhang Qingliang ,Shi Wujie,Shen Rulin | |||
Mathematics 28 October 2009 | |||
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Abstract:Let $G$ be a finite group. We know that E7(q)with connected prime graph is not recognizable by prime graph. Thus in this paper we consider E7(q)with disconnected prime graph. The main result is as follows: the simple group E7(q)with disconnected prime graph is quasirecognizable by prime graph, and furthermore we show that if |G|=|E7(q)| and Γ(G) =Γ(E7(q)), where E7(q)has a disconnected prime graph, then G = E7(q). In fact we give a generalization of some known results of W. Shi for E7(q). | |||
TO cite this article:Zhang Qingliang ,Shi Wujie,Shen Rulin. Quasirecognition by prime graph of the simple group $ E_7(q)$[OL].[28 October 2009] http://en.paper.edu.cn/en_releasepaper/content/36185 |
7. Quasirecognition by prime graph of the simple groups $G_2(q)$ and $^2B_2(q)$ | |||
Zhang Qingliang ,Shi Wujie,Shen Rulin | |||
Mathematics 27 October 2009 | |||
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Abstract:Let G be a finite group. The main result is as follows: if G is a finite group such that Γ(G) = Γ(M), where M is G2(q) (q = 32n+1) or 2B2(q) (q = 22n+1 > 2), then G is quasirecognizable by prime graph. And furthermore we generalize some known results of W. Shi for G2(q) and 2B2(q). | |||
TO cite this article:Zhang Qingliang ,Shi Wujie,Shen Rulin. Quasirecognition by prime graph of the simple groups $G_2(q)$ and $^2B_2(q)$[OL].[27 October 2009] http://en.paper.edu.cn/en_releasepaper/content/36172 |
8. Recognition by spectrum for finite simple groups of Lie type | |||
M.A. Grechkoseeva,Wujie Shi,Andrey V. Vasilev | |||
Mathematics 21 January 2008 | |||
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Abstract:The goal of this paper is to survey new results on the recognition problem. We focus our attention on the methods recently developed in this area. In the last section we review arithmetical characterization of spectra of finite simple groups and conclude with a list of groups for which the recognition problem was solved within last three years. In each section we formulate related open problems. | |||
TO cite this article:M.A. Grechkoseeva,Wujie Shi,Andrey V. Vasilev. Recognition by spectrum for finite simple groups of Lie type[OL].[21 January 2008] http://en.paper.edu.cn/en_releasepaper/content/18241 |
9. Arithmetical Properties of Finite Groups | |||
Shi Wujie | |||
Mathematics 14 June 2006 | |||
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Abstract:Let $G$ be a finite group and $Ch_i(G)$ some quantitative sets. In this paper we study the influence of $Ch_i(G)$ to the structure of $G$. We present a survey of author and his colleagues\ | |||
TO cite this article:Shi Wujie . Arithmetical Properties of Finite Groups[OL].[14 June 2006] http://en.paper.edu.cn/en_releasepaper/content/7139 |
10. Presentations for finite complex reflection | |||
Shi Jian Yi | |||
Mathematics 25 February 2005 | |||
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Abstract:We survey our achievements on the classification of congruence classes of presentations for the finite complex reflection groups. The classification is described in terms of certain graphs for the imprimitive groups, and is based on the computer programmes for the primitive groups. | |||
TO cite this article:Shi Jian Yi. Presentations for finite complex reflection[OL].[25 February 2005] http://en.paper.edu.cn/en_releasepaper/content/1595 |
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