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On permutation representations of polyhedral groups
Authors:B. Sury
Affiliation:School Of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India
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).

Keywords:Permutation representations   triangle groups
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