Integral equivalence of permutation represent ations
نویسندگان
چکیده
This paper presents the author’s heretofore unpublished example of nonisomorphic transitive permutation representations with isomorphic integral permutation modules. Some positive results are also given. This paper is dedicated to the menory of Hans Zassenhaus. Let G be a finite group acting on finite sets R,R’. Recall that R z R’ as G-sets if and only if there is a 1-l correspondence between 0 and R’ commuting with the action of G. Let ZR, ZW denote the associated permutation modules for the group ring ZG. A fundamental question is: Does Zi2 z Zn' imply R = R’? This question was first studied in print by S. B. Conlon [Cl, for intransitive actions, who showed that the answer there is usually negative. As Conlon showed, the intransitive question is really a much easier problem, accessible through the Burnside ‘The au&r thanks NSF for its support
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تاریخ انتشار 1998