The Superimprimitive Subgroups Of The Alternating Group Of Degree 8

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The Superimprimitive Subgroups Of The Alternating Group Of Degree 8

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dc.contributor.author Omar, A. A. H [عبد الرؤوف عمر] en_US
dc.date.accessioned 2009-11-25T15:31:21Z
dc.date.available 2009-11-25T15:31:21Z
dc.date.issued 1984 en_US
dc.identifier.citation Qatar University Science Journal, 1984, Vol. 4, Pages 7-12. en_US
dc.identifier.uri http://hdl.handle.net/10576/10249
dc.description.abstract A transitive permutation group G is called superimprimitive if it is imprimitive with non-trivial block systems of imprimitivity of lengths all the non-trivial divisors of the degree of G; The superimprimitivity concepts was studied first by Omar (2), and later by the authors (3). In the present paper we shall give some results concerning this concept m part 1, and determine in part 2, all superimprimitive subgroups of the alternating group of degree 8. We proved the following: Lemma (I): Let G be a transitive group acting on a set X and m is the number of non-trivial divisors of |X). If G contains m intransitive normal proper subgroups each having different orbit lengths then G is superimprimitive. The orbits of each subgroup form a block system of imprimitivity. Lemma (2): (a) Let G be a superimprimitive group. For every non-trivial divisor d of the degree of G and for x£X, there exists a group Z which lies property between G, and G such that the set {x^ has length d. (b) I^G,CZ,cG holds, where Zi, i=l,...,m are proper subgroups of G and the sets {x '} have different lengths, then G is superimprimitive. Then we show that, among the 48337 subgroups of Ag, which split into 137 classes there are 4425 superimprimitive subgroups which split into 18 classes, their generators are given. en_US
dc.description.abstract يقال لزمرة التبديلات الأنتقالية أنها متعددة غير الأولية اذا كانت غير الأولية ولها نظام من البلوكات الفصلية لكل قاسم فعلي من قواسم درجة الزمرة . ولقد قدم هذا البحث نظريتين لشروط مكافئة للتعريف . للتعرف عل الزمر متعددة غير الأولية . ثم وضحنا أنه بين كل الزمر الجزئية لزمرة التبديلات الزوجية من درجة ثمانية ، م هـ ، وعددهم 48337 زمرة جزئية مقسمين الى 137 فصل تكافؤ . يوجد25 4 4 زمرة جزثية متعددة غيرالأولية مقسمين الى 18 فصل تكافؤ. ar
dc.language.iso en en_US
dc.publisher Qatar University en_US
dc.subject Mathematics en_US
dc.subject الرياضيات ar
dc.title The Superimprimitive Subgroups Of The Alternating Group Of Degree 8 en_US
dc.title.alternative الزمر الجزئية متعددة غير الأولية من الزمرة 8ِأ ar
dc.type Article en_US
dc.identifier.pagination 7-12 en_US
dc.identifier.volume 4 en_US

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