山大新闻网-亚博安卓下载

举办单位：数学科学学院

负责人姓名常学武

电话：18635195429

活动主题：

twisted centrally large subgroups of finite groups

形式：学术报告

活动内容摘要：

let g be a finite group. a subgroup q of g is defined, by glauberman, to be a centrally large subgroup, or cl-subgroup, of g if |q| · |z(q)| ⩾ |q^∗| · |z(q^∗)| for every subgroup q^∗ of g. a cl-subgroup of g that is minimal under inclusion is called a minimal cl-subgroup of g. glauberman[centrally large subgroups of finite p-groups, j. algebra, 300(2006), 480-508] studied some properties of cl-subgroups, especially minimal cl-subgroups. he showed that if q_1 and q_2 are a pair of minimal cl-subgroups, then

q_i= (q_1∩q_2)z(q_i)fori = 1, 2.(∗)

we say that two cl-subgroups q_1 and q_2 (not necessarily minimal) are twisted cl-subgroups if they satisfy the above property (∗). in this paper, we extend glauberman’s work to prove some further properties of cl-subgroups, especially twisted cl-subgroups. in addition, we give a negative answer to a conjecture proposed by scoppola et al. [the chermak-delgado measure in finite p-groups, j. algebra, 502(2018), 262-276].

主讲人基本情况：

安立坚，教授、博士生导师，山西师范大学数学与计算机科学学院院长，山西省数学会副理事长。主要研究方向为群论，在 j. algebra，sci. china math. 等国内外重要刊物上发表论文 20 余篇，出版专著两部，主持国家自然科学基金面上项目 2 项。解决了群论领域若干重要问题，多项成果被著名群论学家 berkovich 和 janko在其专著 (groups of prime power order, 2016) 中评价为“基本结果”。应邀在 2019 年美国召开的国际群论会议上做 50 分钟大会报告。

听众范围：数学学院师生

举办时间：2023-05-19

举办地点：数学106教室

报告类型：理科类