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WEAK CAYLEY TABLE GROUPS OF SOME CRYSTALLOGRAPHIC GROUPS

Part of: Representation theory of groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  28 January 2018

STEPHEN P. HUMPHRIES  and
REBECA A. PAULSEN
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
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Abstract

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For a group G, a weak Cayley table isomorphism is a bijection f : G → G such that f(g1g2) is conjugate to f(g1)f(g2) for all g1, g2 ∈ G. 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.

MSC classification

Primary: 20C15: Ordinary representations and characters
Secondary: 20C05: Group rings of finite groups and their modules 20F28: Automorphism groups of groups
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 3 , September 2018 , pp. 635 - 660
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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