Totally chiral maps and hypermaps of small genus


Breda d'Azevedo, Antonio and Jones, Gareth (2009) Totally chiral maps and hypermaps of small genus Journal of Algebra, 322, (11), pp. 3971-3996. (doi:10.1016/j.jalgebra.2009.02.017).

Download

[img] PDF TotallychiralJAlg.pdf - Version of Record
Download (481kB)

Description/Abstract

An orientably regular hypermap is totally chiral if it and its mirror image have no non-trivial common quotients. We classify the totally chiral hypermaps of genus up to 1001, and prove that the least genus of any totally chiral hypermap is 211, attained by twelve orientably regular hypermaps with monodromy group A7 and type (3,4,4) (up to triality). The least genus of any totally chiral map is 631, attained by a chiral pair of orientably regular maps of type {11,4}, together with their duals; their monodromy group is the Mathieu group M11. This is also the least genus of any totally chiral hypermap with non-simple monodromy group, in this case the perfect triple covering 3.A7 of A7. The least genus of any totally chiral map with non-simple monodromy group is 1457, attained by 48 maps with monodromy group isomorphic to the central extension 2.Sz(8).

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/j.jalgebra.2009.02.017
ISSNs: 0021-8693 (print)
Keywords: map, hypermap, totally chiral map, totally chiral hypermap, chirality group, 2-generated groups
ePrint ID: 156471
Date :
Date Event
1 December 2009Published
Date Deposited: 01 Jun 2010 09:42
Last Modified: 18 Apr 2017 04:01
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/156471

Actions (login required)

View Item View Item