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On generators of crystallographic groups and actions on flat orbifolds

On generators of crystallographic groups and actions on flat orbifolds
On generators of crystallographic groups and actions on flat orbifolds
We find new bounds on the minimal number of generators of crystallographic groups with p-group holonomy. We also show that similar bounds exist on the minimal number of generators of the abelianizations of arbitrary crystallographic groups. As a consequence, we show that this restricts the rank of elementary abelian p-groups that can act effectively on closed connected flat orbifolds.
1433-5883
553-561
Adem, Alejandro
f10ed11e-d609-4a7e-98a2-1e166839f4e6
Dekimpe, Karel
81b4ebfd-4085-40f6-ac33-7077cdf43c75
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
Putrycz, Bartosz
c9ad40c7-b96a-42c0-a238-909351982652
Adem, Alejandro
f10ed11e-d609-4a7e-98a2-1e166839f4e6
Dekimpe, Karel
81b4ebfd-4085-40f6-ac33-7077cdf43c75
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
Putrycz, Bartosz
c9ad40c7-b96a-42c0-a238-909351982652

Adem, Alejandro, Dekimpe, Karel, Petrosyan, Nansen and Putrycz, Bartosz (2012) On generators of crystallographic groups and actions on flat orbifolds. Journal of Group Theory, 15 (4), 553-561. (doi:10.1515/jgt-2012-0005).

Record type: Article

Abstract

We find new bounds on the minimal number of generators of crystallographic groups with p-group holonomy. We also show that similar bounds exist on the minimal number of generators of the abelianizations of arbitrary crystallographic groups. As a consequence, we show that this restricts the rank of elementary abelian p-groups that can act effectively on closed connected flat orbifolds.

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Published date: 2012
Organisations: Pure Mathematics

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Local EPrints ID: 356890
URI: http://eprints.soton.ac.uk/id/eprint/356890
DOI: doi:10.1515/jgt-2012-0005
ISSN: 1433-5883
PURE UUID: 7a4f1ec1-2216-4a7c-aeeb-7770daa5dfe2
ORCID for Nansen Petrosyan: ORCID iD orcid.org/0000-0002-2768-5279

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Date deposited: 20 Sep 2013 15:44
Last modified: 15 Mar 2024 03:49

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Contributors

Author: Alejandro Adem
Author: Karel Dekimpe
Author: Nansen Petrosyan ORCID iD
Author: Bartosz Putrycz

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