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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On permutation representations
of polyhedral groups


Author: B. Sury
Journal: Proc. Amer. Math. Soc. 127 (1999), 1973-1974
MSC (1991): Primary 20B05
Published electronically: March 16, 1999
MathSciNet review: 1486753
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Abstract | References | Similar Articles | Additional Information

Abstract: We answer affirmatively the following question of Derek Holt: Given integers $l,m,n \geq 2$, can one, in a simple manner, find a finite set $\Omega$ and permutations $a,b$ such that $a$ has order $l$, $b$ has order $m$ and $ab$ has order $n$? The method of proof enables us to prove more general results (Theorems 2 and 3).


References [Enhancements On Off] (What's this?)

  • [D] Derek Holt, Problem 22 of the Problems Book, Group Pub Forum Home Page, group-pub-forum at maths.bath.ac.uk
  • [M] G.A.Miller, `Groups defined by the orders of two generators and the order of their product', Amer.J.Math. 24 (1902), 96-100.

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Additional Information

B. Sury
Affiliation: School Of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India
Email: sury@math.tifr.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04818-2
PII: S 0002-9939(99)04818-2
Keywords: Permutation representations, triangle groups
Received by editor(s): October 15, 1997
Published electronically: March 16, 1999
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1999 American Mathematical Society