Geodesic
WEAK CAYLEY TABLE GROUPS OF SOME CRYSTALLOGRAPHIC GROUPS
Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 635-660

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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. 
HUMPHRIES, STEPHEN P.; PAULSEN, REBECA A. WEAK CAYLEY TABLE GROUPS OF SOME CRYSTALLOGRAPHIC GROUPS. Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 635-660. doi: 10.1017/S0017089517000337
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     journal = {Glasgow mathematical journal},
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[1] 1. Curtis, C. W., Pioneers of representation theory: Frobenius, Burnside, Schur, and Brauer. History of mathematics, vol. 15 (American Mathematical Society, Providence, RI; London Mathematical Society, London, 1999), 287 pages. Google Scholar

[2] 2. Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras. (AMS Chelsea Publishing, Providence, RI, 2006). Reprint of the 1962 original. Google Scholar

[3] 3. Feit, W., Characters of finite groups (W. A. Benjamin, New York-Amsterdam 1967), viii+186 pp. Google Scholar

[4] 4. Gonçalves, D. and Wong, P., Automorphisms of the two dimensional crystallographic groups, Comm. Algebra 42 (2) (2014), 909–931. Google Scholar

[5] 5. Humphries, S. P., Weak Cayley table groups, J. Algebra 216 (1999), 135–158. Google Scholar

[6] 6. Humphries, S. P. and Long, N., Weak Cayley table groups: Alternating and coxeter groups, Comm. Algebra 43 (11) (2015), 4763–4782. Google Scholar | DOI

[7] 7. Humphries, S. P. and Long, N., Weak Cayley table groups III: PSL(2,q), Comm. Algebra 45 (7) (2017), 3110–3136. Google Scholar

[8] 8. Iversen, B., Lectures on crystallographic groups. Lecture notes series, vol. 60 (Aarhus Universitet, Matematisk Institut, Aarhus, 1990), vi+144. Google Scholar

[9] 9. Janssen, T., Crystallographic groups (North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973), xiii+281. Google Scholar

[10] 10. Johnson, K. W., Mattarei, S. and Sehgal, S. K., Weak Cayley tables, J. Lond. Math. Soc. 61 (2000), 395–411. Google Scholar

[11] 11. Bosma, W. and Cannon, J., MAGMA (University of Sydney, 1994). Google Scholar

[12] 12. Magnus, W., Karrass, S., and Solitar, D., Combinatorial group theory (Dover, New York, 1976). Google Scholar

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