The multiple holomorph of centerless groups

讲座时间 Datetime: 2021年7月15日，星期四， 15:00-16:00

地点 Venue: Zoom，489 809 3801

报告人 Speaker:  曾善谊 助理教授

单位 Affiliation: 日本御茶水女子大学

报告摘要 Abstract:

The holomorph $\mathrm{Hol}(G)$ of a group $G$ may be defined as the normalizer of the subgroup of left translations in the group of all permutations of $G$. The multiple holomorph $\mathrm{NHol}(G)$ of $G$ may in turn be defined as the normalizer of the holomorph. Their quotient $T(G) = \mathrm{NHol}(G)/\mathrm{Hol}(G)$ has been computed for various families of groups $G$, and interestingly $T(G)$ turns out to be elementary $2$-abelian in many of the known cases. In this talk, we consider the case when $G$ is centerless, and we will present our new result that $T(G)$ has to be elementary $2$-abelian unless $G$ satisfies some fairly strong conditions.