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Title: Highest rank of a polytope for An
Author: Cameron, Peter
Leemans, Dimitri
Mixer, Mark
Fernandes, Maria Elisa
Keywords: Abstract Regular Polytopes
String C-Groups
Alternating Groups
Permutation Groups
Issue Date: 2017
Publisher: London Mathematical Society
Abstract: We prove that the highest rank of a string C-group constructed from an alternating group An is 3 if n = 5; 4 if n = 9; 5 if n = 10; 6 if n = 11; and the floor of of (n-1)/2 if n>=12. Moreover, if n = 3; 4; 6; 7 or 8, the group An is not a string C-group. This solves a conjecture made by the last three authors in 2012.
Peer review: yes
DOI: 10.1112/plms.12039
ISSN: 0024-6115
Appears in Collections:CIDMA - Artigos
AGG - Artigos

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