Top-nilpotent enveloping semigroups and pro-nilsystems

Jiahao Qiu; Jianjie Zhao

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arXiv · 1911.05435

Top-nilpotent enveloping semigroups and pro-nilsystems

Jiahao Qiu·Jianjie Zhao

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Abstract

In this paper, it is shown that for $d\in\mathbb{N}$, a minimal system $(X,T)$ is a $d$-step pro-nilsystem if its enveloping semigroup is a $d$-step top-nilpotent group, answering an open question by Donoso. Thus, combining the previous result of Donoso, it turns out that a minimal system $(X,T)$ is a $d$-step pro-nilsystem if and only if its enveloping semigroup is a $d$-step top-nilpotent group.

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Jiahao Qiu, Jianjie Zhao. 2019-11-13. Top-nilpotent enveloping semigroups and pro-nilsystems. https://arxiv.org/abs/1911.05435

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