The discrete elementary groups

Qing Zhou

The discrete elementary groups

Qing Zhou^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

This paper discusses discrete elementary subgroups in the Mobius group M(R ̂ⁿ). With a help of geometry, it is proved that these groups are isomorphic to either a group extension of Z by a finite subgroup of SO(n) or an extension of a finite group by a free Abelian group of rank k ≤ n.

Original language	English
Pages (from-to)	1047-1053
Number of pages	7
Journal	Science in China Series A-Mathematics Physics Astronomy and Technological Science
Volume	36
Issue number	9
State	Published - Sep 1993

Keywords

Bieberbach group
Euclidean geometry orbifold
Mobius group
elementary group

Cite this

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abstract = "This paper discusses discrete elementary subgroups in the Mobius group M(R{\^ }n). With a help of geometry, it is proved that these groups are isomorphic to either a group extension of Z by a finite subgroup of SO(n) or an extension of a finite group by a free Abelian group of rank k ≤ n.",

keywords = "Bieberbach group, Euclidean geometry orbifold, Mobius group, elementary group",

author = "Qing Zhou",

year = "1993",

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AB - This paper discusses discrete elementary subgroups in the Mobius group M(R ̂n). With a help of geometry, it is proved that these groups are isomorphic to either a group extension of Z by a finite subgroup of SO(n) or an extension of a finite group by a free Abelian group of rank k ≤ n.

KW - Bieberbach group

KW - Euclidean geometry orbifold

KW - Mobius group

KW - elementary group

UR - https://www.scopus.com/pages/publications/21644478392

M3 - 文章

AN - SCOPUS:21644478392

SN - 1001-6511

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JO - Science in China Series A-Mathematics Physics Astronomy and Technological Science

JF - Science in China Series A-Mathematics Physics Astronomy and Technological Science

IS - 9

ER -

The discrete elementary groups

Abstract

Keywords

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