On permutation representations of polyhedral groups
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- by B. Sury
- Proc. Amer. Math. Soc. 127 (1999), 1973-1974
- DOI: https://doi.org/10.1090/S0002-9939-99-04818-2
- Published electronically: March 16, 1999
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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
- Derek Holt, Problem 22 of the Problems Book, Group Pub Forum Home Page, group-pub-forum at maths.bath.ac.uk
- G.A.Miller, ‘Groups defined by the orders of two generators and the order of their product’, Amer.J.Math. 24 (1902), 96-100.
Bibliographic 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
- Received by editor(s): October 15, 1997
- Published electronically: March 16, 1999
- Communicated by: Ronald M. Solomon
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1973-1974
- MSC (1991): Primary 20B05
- DOI: https://doi.org/10.1090/S0002-9939-99-04818-2
- MathSciNet review: 1486753