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Some properties of generalized wreath products

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Some properties of generalized wreath products COMPOSITIO MATHEMATICA MARTYNDIXON THOMASA. FOURNELLE Some properties of generalizedwreath products Compositio Mathematica, tome 52, no 3 (1984), p. 355-372. <http://www.numdam.org/item?id=CM_1984__52_3_355_0> © Foundation Compositio Mathematica, 1984, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions gé- nérales d’utilisation (http://www.numdam.org/legal.php). Toute utilisa- tion commerciale ou impression systématique est constitutive d’une in- fraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ 355 SOME PROPERTIES OF GENERALIZED WREATH PRODUCTS Martyn Dixon and Thomas A. Fournelle Compositio Mathematica 52 (1984) 355-372 © 1984 Martinus Nijhoff Publishers, The Hague. Printed in The Netherlands 1. Introduction The concept of a wreath product of permutation groups has been well documented in the literature. Kaluznin and Krasner introduced the idea in [6] in order to obtain groups with a certain universal property. Various other results were established in [6], for wreath products of finitely many groups. Wreath products with an infinite number of factors were dis- cussed in [2] and [8]. The approach used there was to write the wreath product as a union of finite wreath products, with a suitable embedding rule. Hall in [3] approached the problem of a wreath product of infinitely many permutation groups in a different manner. His construction in- volved defining the wreath product directly as a subgroup of the symmet- ric group on a suitably chosen set. The wreath product obtained was "restricted", in some sense. Moreover, Hall only considered wreath products of groups indexed by totally ordered sets. Hall used his results to construct various

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