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A Generalization of Totally Imprimitive Permutation Groups | ||
| International Journal of Group Theory | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 مرداد 1405 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2026.148234.2014 | ||
| نویسنده | ||
| Rümeysa Sacide Altınkaya* | ||
| Department of Math, Faculty of Science, Gazi University, 06500 Teknikokullar, Ankara, Türkiye | ||
| چکیده | ||
| In the present paper, we investigate a general form of totally imprimitive finitary permutation groups. Totally imprimitive groups were originally defined by P. M. Neumann for subgroups of the finitary symmetric group acting on an infinite set. We aim to extend this definition to arbitrary subgroups of symmetric groups, which are not necessarily finitary. To this end, we introduce a property that we shall call the support-block property for subgroups of symmetric groups. This property allows us to generalize several results previously obtained for totally imprimitive finitary permutation groups to a broader class of permutation groups acting on infinite sets. We recover and extend various structural results obtained in earlier studies, with particular emphasis on transitive permutation groups. Moreover, we reconstruct an example arising in previous studies on finitary permutation groups and show that it satisfies the support-block property, illustrating the applicability of our approach. Several consequences and applications of this framework are also discussed. | ||
| کلیدواژهها | ||
| Support-Block Property (SBP)؛ totally imprimitive group؛ permutation group؛ finitary permutation group | ||
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آمار تعداد مشاهده مقاله: 29 |
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