李型单群的内对角自同构的阶

Pub Date : 2022-07-27 DOI:10.1515/jgth-2021-0192

A. Buturlakin, M. A. Grechkoseeva

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引用次数: 2

摘要

摘要:我们把有限群𝐺的元素阶的集合称为𝐺的谱。对于简单群PSL n n (q) \ mathm {PSL}_{n}(q)， PSU n n (q) \ mathm {PSU}_{n}(q)， e6 (q)， e6 2 (q) {}^{2}E_{6}(q)，我们用对角自同构描述了这些群的扩展谱。

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Orders of inner-diagonal automorphisms of some simple groups of Lie type

Abstract We refer to the set of element orders of a finite group 𝐺 as the spectrum of 𝐺. For the simple groups PSL n ⁢ ( q ) \mathrm{PSL}_{n}(q) , PSU n ⁢ ( q ) \mathrm{PSU}_{n}(q) , E 6 ⁢ ( q ) E_{6}(q) , and E 6 2 ⁢ ( q ) {}^{2}E_{6}(q) , we describe the spectra of extensions of these groups by diagonal automorphisms.

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