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L15（2）的新刻画
  • ISSN号：1003-3998
  • 期刊名称：《数学物理学报：A辑》
  • 时间：0
  • 分类：O152.1[理学—数学;理学—基础数学]
  • 作者机构：[1]重庆大学数学与统计学院重庆沙坪坝401331
  • 相关基金：国家自然科学基金（11271301,11171364,10871032）和国家自然科学青年基金项目（11001226）资助
作者： 张良才[1], 张苗[1], 聂文敏[1]
关键词： 有限单群, 素图, 顶点度数, 素图度数序列, Finite simple group, Prime graph, Degree of a vertex, Degree pattern.
中文摘要：

对于任意一个有限群G,令π（G）表示由它的阶的所有素因子所构成的集合.该文构建一种与之相关的简单图,称之为素图,记作Г（G）.该图的顶点集合是π（G）,图中两顶点p,q相连（记作p～q）的充要条件是群G恰有Pq阶元[7 5].令π（G）={p1,P2,…,ps}.对于任意p∈π（G）,令deg（p）∶=｜{q∈π（G）｜在素图Г（G）中,p～q}｜,并称之为顶点p的度数.同时,我们定义D（G）∶=（deg（p1）,deg（p2）,…,deg（ps））,其中p1＜P2＜…＜ps,并称之为群G的素图度数序列.若存在k个互不同构的群与群G具有相同的群阶和素图度数序列,则称群G是可k-重OD-刻画的.特别地,可1-重OD-刻画的群也称为可OD-刻画的群[11].在该文中,引入一个新的引理并证明了特殊射影线性群L15（2）是可OD-刻画的.作为一个推论,得到L15（2）是可OG-刻画的.该方法也可适用于其它一些具体的有限单群.

英文摘要：

If G is a finite group, we define its prime graph F（G） as follows. The vertices of F（G） are the primes dividing the order of G and two distinct vertices p, q are joined by an edge, denoted by p N q, if and only if there is an element in G of order pq （see [7, 15]）. Ozk Assume IGI = plp2...pk with primes pl 〈 P2 〈 〈 Pk and natural numbers ai. For p {Pl,Pa, ,Pk}, define deg（p） ：= [{q e 7r（G）[q p}[, which is called the degree of p. We also define D（G） ：= （deg（pl）, deg（p2）,＇, deg（pk））, which is called the degree pattern of the group G. We say a group G is t-fold OD-characterizable if there exist exactly t non- isomorphic finite groups M such that IMI = IGI and D（M） D（G） （see [11]）. In particular, a 1-fold OD-characterizable group is simply called an OD-characterizable group. In the present paper, we prove that the projective special linear group L15 （2） is OD-eharacterizable by a newly introduced lemma to deal with its connected prime graph. As a consequence of this result, we obtain that L15（2） is OG-eharaeterizable.

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期刊信息
  • 《数学物理学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国科学院武汉物理与数学研究所
  • 主编：李邦河 陈贵强 朱熹平
  • 地址：湖北省武汉市武昌小洪山西路30号武汉71010信箱
  • 邮编：430071
  • 邮箱：actams@wipm.ac.cn
  • 电话：027-87199206
  • 国际标准刊号：ISSN：1003-3998
  • 国内统一刊号：ISSN：42-1226/O
  • 邮发代号:38-214
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  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:5382