{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T07:14:45Z","timestamp":1649056485898},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,6]]},"abstract":"<jats:p> The conjugacy classes of any group are important since they reflect some aspects of the structure of the group. The construction of the conjugacy classes of finite groups has been a subject of research for several authors. Let n,m be positive integers and [Formula: see text] be the direct product of m copies of the symmetric group S<jats:sub>n<\/jats:sub> of degree n. Then [Formula: see text] is a subgroup of the symmetric group S<jats:sub>mn<\/jats:sub> of degree m \u00d7 n. Let g\u2208S<jats:sub>mn<\/jats:sub>, of type [m<jats:sup>n<\/jats:sup>] where each m-cycle contains one symbol from each set of symbols in that order on which the copies of S<jats:sub>n<\/jats:sub> act. Then g permutes the elements of the copies of S<jats:sub>n<\/jats:sub> in [Formula: see text] and generates a cyclic group C<jats:sub>m<\/jats:sub> = \u3008g\u3009 of order m. The wreath product of S<jats:sub>n<\/jats:sub> with C<jats:sub>m<\/jats:sub> is a split extension or semi-direct product of [Formula: see text] by C<jats:sub>m<\/jats:sub>, denoted by [Formula: see text]. It is clear that [Formula: see text] is a subgroup of the symmetric group S<jats:sub>mn<\/jats:sub>. In this paper we give a method similar to coset analysis for constructing the conjugacy classes of [Formula: see text], where m is prime. Apart from the fact that this is an alternative method for constructing the conjugacy classes of the group [Formula: see text], this method is useful in the construction of Fischer\u2013Clifford matrices of the group [Formula: see text]. These Fischer\u2013Clifford matrices are useful in the construction of the character table of [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196708004573","type":"journal-article","created":{"date-parts":[[2008,6,24]],"date-time":"2008-06-24T05:38:40Z","timestamp":1214285920000},"page":"705-717","source":"Crossref","is-referenced-by-count":0,"title":["THE CONJUGACY CLASSES OF A SUBGROUP $S_{n}^{m} : C_{m}$ OF S<sub>mn<\/sub>, prime m"],"prefix":"10.1142","volume":"18","author":[{"given":"KENNETH","family":"ZIMBA","sequence":"first","affiliation":[{"name":"University of Limpopo, Private Bag X1106, Sovenga 0727, Polokwane, South Africa"}]},{"given":"MERIAM","family":"RABOSHAKGA","sequence":"additional","affiliation":[{"name":"University of Limpopo, Private Bag X1106, Sovenga 0727, Polokwane, South Africa"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"155","volume":"38","author":"Al-Ali M. I. M.","journal-title":"Math. Japonica"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1994-1208219-2"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.2307\/1968599"},{"key":"rf5","series-title":"Progr. Math.","first-page":"1","volume":"95","author":"Fischer B.","year":"1991"},{"key":"rf7","volume-title":"Character Theory of Finite Groups","author":"Isaac I. M.","year":"1976"},{"key":"rf8","volume-title":"A First Course in Abstract Algebra","author":"Rotman J. J.","year":"1996"},{"key":"rf9","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0067943","volume-title":"Representations of Permutation Groups I, Vol. 1","volume":"240","author":"Kerber A.","year":"1971"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-99-01157-6"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1080\/16073606.1999.9632080"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.2989\/16073600509486123"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196708004573","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:43:12Z","timestamp":1565170992000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196708004573"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6]]},"references-count":10,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,6]]}},"alternative-id":["10.1142\/S0218196708004573"],"URL":"https:\/\/doi.org\/10.1142\/s0218196708004573","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,6]]}}}