String C-groups as transitive subgroups of Sn

Peter Jephson Cameron; Maria Elisa Fernandes; Dimitri Leemans; Mark Mixer

doi:10.1016/j.jalgebra.2015.09.040

String C-groups as transitive subgroups of S_n

Peter Jephson Cameron, Maria Elisa Fernandes, Dimitri Leemans, Mark Mixer

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

Abstract

If Γ is a string C-group which is isomorphic to a transitive subgroup of the symmetric group S_n (other than S_n and the alternating group A_n), then the rank of Γ is at most n/2+1, with finitely many exceptions (which are classified). It is conjectured that only the symmetric group has to be excluded.

Original language	English
Pages (from-to)	468-478
Journal	Journal of Algebra
Volume	447
Early online date	9 Nov 2015
DOIs	https://doi.org/10.1016/j.jalgebra.2015.09.040
Publication status	Published - 1 Feb 2016

Keywords

Regular polytope
String C-group
Transitive permutation group

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10.1016/j.jalgebra.2015.09.040

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© 2015, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.sciencedirect.com / https://dx.doi.org/10.1016/j.jalgebra.2015.09.040
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Cite this

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title = "String C-groups as transitive subgroups of Sn",

abstract = "If Γ is a string C-group which is isomorphic to a transitive subgroup of the symmetric group Sn (other than Sn and the alternating group An), then the rank of Γ is at most n/2+1, with finitely many exceptions (which are classified). It is conjectured that only the symmetric group has to be excluded.",

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AU - Fernandes, Maria Elisa

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AU - Mixer, Mark

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AB - If Γ is a string C-group which is isomorphic to a transitive subgroup of the symmetric group Sn (other than Sn and the alternating group An), then the rank of Γ is at most n/2+1, with finitely many exceptions (which are classified). It is conjectured that only the symmetric group has to be excluded.

KW - Regular polytope

KW - String C-group

KW - Transitive permutation group

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ER -

String C-groups as transitive subgroups of S_n

Abstract

Keywords

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