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WEAK CAYLEY TABLE GROUPS OF SOME CRYSTALLOGRAPHIC GROUPS

Published online by Cambridge University Press:  28 January 2018

STEPHEN P. HUMPHRIES
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA e-mail: steve@mathematics.byu.edu, lakabecky@gmail.com
REBECA A. PAULSEN
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA e-mail: steve@mathematics.byu.edu, lakabecky@gmail.com

Abstract

For a group G, a weak Cayley table isomorphism is a bijection f : GG such that f(g1g2) is conjugate to f(g1)f(g2) for all g1, g2G. The set of all weak Cayley table isomorphisms forms a group (G) that is the group of symmetries of the weak Cayley table of G. We determine (G) for each of the 17 wallpaper groups G, and for some other crystallographic groups.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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