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Alternating Quotients of the (3,q,r) Triangle Groups

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Publication details

JournalCommunications in Algebra
DatePublished - 1997
Number of pages16
Pages (from-to)1817-1832
Original languageUndefined/Unknown


A long standing conjecture (attributed to Graham Higman) asserts that each of the triangle groups △(p,q,r)for 1/p+1/q+1/r>1 contains among its homomorphic images all but finitely many of the alternating or symmetric groups. This phenomenon has been termed property H by Mushtaq and Servatius [9]. The work of several authors over the last decade and a half has shown that for any value of q, there are only finitely many r such that △(2,q,r) fails to have property H. In this paper, the techniques used by these authors are generalised to handle the possinblity that p is odd, and as a result, it is shown that for any q≧3, there are only finitely many r such that △(3,q,r)fails to have property H.

    Research areas

  • Algebra, Pure Mathematics

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