A relationship between the finite group Sp = T2 = (ST)q = E and the (p, q)-completability of disk-decompositions
✍ Scribed by Mirko Horňák
- Publisher
- John Wiley and Sons
- Year
- 1983
- Tongue
- English
- Weight
- 537 KB
- Volume
- 110
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Cell-decorril)ositioiis of the sphere whose faces are mdti-p-gonaZ (having a multiple of p edges) and vertices are tnulti-q-zlalent (incident with a multiple of q edges), with a sinall number of p-exceptiowl (non-multi-p-gonal) faces and q-exreptional (non-multi-q-valent) vertices, were intensively studied by many authorssee CROWE "4, GALLA1 [3], GRVNRAUM [4], HORBBK [5], HORRAK-JUCOVI~ [8].
JENDROL' [9], MATXEVITCH [13], MOTZKIK L141.
A great part of their results concerns existence questions. Jn correspondence with this in HORAAK [6] the following notion was introduced : A disk-decomposition (cell-decomposition of a topological disk) D is said t o he ( p , 9)-compZetabZe i f there exists a sphere-decomposition B' such that U is its sul,decoin~)osition, every p-exceptional face of D' I)elongs to L) and every p-exceptional vertex of D' is an interior \ ertex of D. In H O R ~L K [6,7] n necessary and sufficient condition of the ( p , q)-coini)leta~)ility is given for every disk-decompositiori and every pair ( p , (I) such that ( p -2) ( q -2) . . = 4. The aim of the present paper is to show a relationship between the finite group with the abstract definition S p = ! P = ( A Y T ) ~= E and the (y~, q)-completaMity of disk-deroin~)ositions for mentioned pairs ( p , (I). For this purpose we shall need some notions, notations and results from [6] and [7]: they are ljresented in the following section. P . J . 8a.fdrik University Deportment of geometry und Algebra iiiiwestie Februrirociho vit'azstva Y 011 5-i Kodice Czeehoc~lovnkin