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AUTOMORPHISM GROUPS OF THE IMPRIMITIVE COMPLEX REFLECTION GROUPS

Part of: Metric geometry Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  01 February 2009

JIAN-YI SHI  and
LI WANG
JIAN-YI SHI*
Affiliation:
Department of Mathematics, East China Normal University, Shanghai, 200241, PR China (email: [email protected])
LI WANG
Affiliation:
Mathematical and Science College, Shanghai Normal University, Shanghai, 200234, PR China (email: [email protected])
*
✉For correspondance.
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Abstract

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We describe the group of all reflection-preserving automorphisms of an imprimitive complex reflection group. We also study some properties of this automorphism group.

Keywords

reflectionsimprimitive complex reflection groupsautomorphism groups

MSC classification

Secondary: 20F28: Automorphism groups of groups 20E36: Automorphisms of infinite groups 51F15: Reflection groups, reflection geometries
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 1 , February 2009 , pp. 123 - 138
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

Supported by the NSF of China, the SFUDP of China, Sino-Germany Centre (GZ310), PCSIRT and Shanghai Leading Academic Discipline Project (BH07).

References

[1]Broué, M., Malle, G. and Rouquier, R., ‘Complex reflection groups, braid groups, Hecke algebras’, J. Reine Angew. Math. 500 (1998), 127–190.Google Scholar
[2]Cohen, A. M., ‘Finite complex reflection groups’, Ann. Sci. École Norm. Sup. (4) 9 (1976), 379–436.CrossRefGoogle Scholar
[3]Franzsen, B. and Howlett, B. R., ‘Automorphisms of nearly finite Coxeter groups’, Adv. Geom. 3 (2003), 301–338.Google Scholar
[4]Hulpke, A., Homomorphism Search, Module of computer software package available at http://www.gap-system.org.Google Scholar
[5]Shephard, G. C. and Todd, J. A., ‘Finite unitary reflection groups’, Canad. J. Math. 6 (1954), 274–304.CrossRefGoogle Scholar
[6]Shi, J. Y., ‘Simple root systems and presentations for certain complex reflection groups’, Comm. Algebra 33 (2005), 1765–1783.Google Scholar
[7]Shi, J. Y., ‘Congruence classes of presentations for the complex reflection groups G(m,1,n) and G(m,m,n)’, Indag. Math. (N.S.) 16(2) (2005), 267–288.CrossRefGoogle Scholar
[8]Shi, J. Y., ‘Congruence classes of presentations for the complex reflection groups G(m,p,n)’, J. Algebra 284(1) (2005), 392–414.CrossRefGoogle Scholar