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On proulx's four exceptional toroidal groups
Author(s) -
Tucker Thomas W.
Publication year - 1984
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190080104
Subject(s) - mathematics , quotient , combinatorics , cayley graph , torus , euclidean space , euclidean geometry , group (periodic table) , toroid , graph , pure mathematics , geometry , physics , plasma , quantum mechanics
V. K. Proulx has proved that every finite group having a Cayley graph embeddable in the torus is, with four unresolved exceptions, a quotient of a Euclidean space group. It was conjectured that these four unresolved groups are not exceptional, that they in fact are Euclidean space‐group quotients. It is shown here that one is not exceptional, but the other three are.