A Black-Box Group Algorithm for Recognizing Finite Symmetric and Alternating Groups, I

R. Beals, C.R. Leedham-Green, Alice Niemeyer, Cheryl Praeger, Akos Seress

    Research output: Contribution to journalArticle

    21 Citations (Scopus)

    Abstract

    We present a Las Vegas algorithm which, for a given black-box group known to be isomorphic to a symmetric or alternating group, produces an explicit isomorphism with the standard permutation representation of the group. This algorithm has applications in computations with matrix groups and permutation groups.In this paper, we handle the case when the degree n of the standard permutation representation is part of the input. In a sequel, we shall treat the case when the value of n is not known in advance.As an important ingredient in the theoretical basis for the algorithm, we prove the following result about the orders of elements of S-n: the conditional probability that a random element σ ξ Sn is an element of S-n is an n-cycle, given that σn = 1, is at least 1/10.
    Original languageEnglish
    Pages (from-to)2097-2113
    JournalTransactions of the American Mathematical Society
    Volume355
    Issue number5
    DOIs
    Publication statusPublished - 2003

    Fingerprint

    Alternating group
    Black Box
    Symmetric group
    Permutation Representation
    Finite Group
    Random Element
    Matrix Groups
    Permutation group
    Conditional probability
    Isomorphism
    Isomorphic
    Cycle
    Standards

    Cite this

    Beals, R. ; Leedham-Green, C.R. ; Niemeyer, Alice ; Praeger, Cheryl ; Seress, Akos. / A Black-Box Group Algorithm for Recognizing Finite Symmetric and Alternating Groups, I. In: Transactions of the American Mathematical Society. 2003 ; Vol. 355, No. 5. pp. 2097-2113.
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    A Black-Box Group Algorithm for Recognizing Finite Symmetric and Alternating Groups, I. / Beals, R.; Leedham-Green, C.R.; Niemeyer, Alice; Praeger, Cheryl; Seress, Akos.

    In: Transactions of the American Mathematical Society, Vol. 355, No. 5, 2003, p. 2097-2113.

    Research output: Contribution to journalArticle

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