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    Properties of the symmetric groups Sn (n≤7) acting on unordered triples

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    Date
    2012-08
    Author
    Kamuti, I.N.
    Kibet, S. K.
    Kerich, G.
    Kimutai, A.
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    Abstract
    In this paper, we investigated some properties associated with the action of symmetric group Sn (n≤7) acting on X(3). If Gx is the stabilizer of the lengths of the orbits of Gx on X are called sub-degrees and the numbers of orbits are called ranks. Ranks and sub-degrees of symmetric groups Sn (n=1, 2, ----) acting on 2-elements subsets from the set X= (1, 2, ---, n) have been calculated by Higman (1970). He showed that the rank is 3 and the sub-degrees are. Therefore, we extend these calculations to the specific symmetric groups Sn (n≤7) acting on X (3).
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    http://ir-library.ku.ac.ke/handle/123456789/8773
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