| OD-characterization of Almost Simple Groups Related to U3（5） |
| |
| 引用本文： | Liang Cai ZHANG,Wu Jie SHI. OD-characterization of Almost Simple Groups Related to U3（5）[J]. 数学学报(英文版), 2010, 26(1): 161-168. DOI: 10.1007/s10114-010-7613-x |
| |
| 作者姓名： | Liang Cai ZHANG Wu Jie SHI |
| |
| 作者单位： | [1]School of Mathematical Sciences, Suzhou University, Suzhou 215006, P. R. China [2]College of Mathematics and Physics, Chongqing University, Shapingba 400044, P. R. China |
| |
| 基金项目： | Supported by National Natural Science Foundation of China （Grant No. 10871032）, the SRFDP of China （Grant No. 20060285002） and a subproject of National Natural Science Foundation of China （Grant No. 50674008） （Chongqing University, Nos. 104207520080834, 104207520080968） Acknowledegements The authors would like to thank the referee for his/her valuable advice. |
| |
| 摘 要： | Let G be a finite group with order ｜G｜=p1^α1p2^α2……pk^αk, where p1 〈 p2 〈……〈 Pk are prime numbers. One of the well-known simple graphs associated with G is the prime graph （or Gruenberg- Kegel graph） denoted .by г（G） （or GK（G））. This graph is constructed as follows： The vertex set of it is π（G） = {p1,p2,…,pk} and two vertices pi, pj with i≠j are adjacent by an edge （and we write pi - pj） if and only if G contains an element of order pipj. The degree deg（pi） of a vertex pj ∈π（G） is the number of edges incident on pi. We define D（G） ：= （deg（p1）, deg（p2）,..., deg（pk））, which is called the degree pattern of G. A group G is called k-fold OD-characterizable if there exist exactly k non- isomorphic groups H such that ｜H｜ = ｜G｜ and D（H） = D（G）. Moreover, a 1-fold OD-characterizable group is simply called OD-characterizable. Let L ：= U3（5） be the projective special unitary group. In this paper, we classify groups with the same order and degree pattern as an almost simple group related to L. In fact, we obtain that L and L.2 are OD-characterizable; L.3 is 3-fold OD-characterizable; L.S3 is 6-fold OD-characterizable.
|
| 关 键 词： | 外径 单群 特性 射影特殊酉群 顶点集 简单图形 有限群 素数 |
OD-characterization of almost simple groups related to U 3(5) |
| |
| Liang Cai Zhang,Wu Jie Shi. OD-characterization of almost simple groups related to U 3(5)[J]. Acta Mathematica Sinica(English Series), 2010, 26(1): 161-168. DOI: 10.1007/s10114-010-7613-x |
| |
| Authors: | Liang Cai Zhang Wu Jie Shi |
| |
| Affiliation: | 1. School of Mathematical Sciences, Suzhou University, Suzhou, 215006, P. R. China
2. College of Mathematics and Physics, Chongqing University, Shapingba, 400044, P. R. China
|
| |
| Abstract: | Let G be a finite group with order |G| = p 1 α1 p 2 α2 … p k αk , where p 1 < p 2 < … < p k are prime numbers. One of the well-known simple graphs associated with G is the prime graph (or Gruenberg-Kegel graph) denoted by Γ(G) (or GK(G)). This graph is constructed as follows: The vertex set of it is π(G) = {p 1, p 2, …, p k } and two vertices p i , p j with i ≠ j are adjacent by an edge (and we write p i ∼ p j ) if and only if G contains an element of order p i p j . The degree deg(p i ) of a vertex p i ∈ π(G) is the number of edges incident on p i . We define D(G):= (deg(p 1), deg(p 2), …, deg(p k )), which is called the degree pattern of G. A group G is called k-fold OD-characterizable if there exist exactly k nonisomorphic groups H such that |H| = |G| and D(H) = D(G). Moreover, a 1-fold OD-characterizable group is simply called OD-characterizable. Let L:= U 3(5) be the projective special unitary group. In this paper, we classify groups with the same order and degree pattern as an almost simple group related to L. In fact, we obtain that L and L.2 are OD-characterizable; L.3 is 3-fold OD-characterizable; L.S 3 is 6-fold OD-characterizable. |
| |
| Keywords: | almost simple group prime graph degree of a vertex degree pattern |
| 本文献已被 维普 SpringerLink 等数据库收录！ |
|
