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dc.contributor.authorKamuti, I.N.
dc.date.accessioned2013-12-17T08:56:05Z
dc.date.available2013-12-17T08:56:05Z
dc.date.issued2011-12
dc.identifier.citationInternational Mathematical F orum, Vol. 7, 2012, no. 30, 1491 - 1494en_US
dc.identifier.urihttp://ir-library.ku.ac.ke/handle/123456789/8076
dc.description.abstractIf M and H are permutation groups with cycle indices ZM and ZH respectively, and if * is some binary operation on permutation groups, then a fundamental problem in enumerative combinatorics is the determination of a formula for ZM *H in terms of ZM and ZH. To this end, a number of results have already been obtained (cf. Harary [1], [2], [3]; Harary and Palmer [6]; Harrison and High [7]; Pόlya [10]). This paper may be viewed as a continuation of a previous paper (Kamuti [8]) in which I have shown how the cycle index of a semidirect product group G= M×H can be expressed in terms of the cycle indices of M and H by considering semidirect products called Frobenius groups. Thus if G=M×H (internal direct product), the aim of this paper is to express the cycle index of G in terms of the cycle indices of M and H when G acts on the cosets of H in G.en_US
dc.language.isoenen_US
dc.publisherInternational Mathematical Forumen_US
dc.subjectInternal direct producten_US
dc.subjectEquivalent actionsen_US
dc.subjectCycle indicesen_US
dc.titleCycle Index of Internal Direct Product Groupsen_US
dc.typeArticleen_US


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