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Rational permutation groups containing a full cycle

Date
2013
Author
Yilmazturk, Utku
Erkoc, Temha
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Abstract
A finite group whose irreducible complex characters are rational valued is called a rational group. Thus, G is a rational group if and only if N (G) (aOE (c) x >)/C (G) (aOE (c) x >) a parts per thousand OE Aut(aOE (c) x >) for every x a G. For example, all symmetric groups and their Sylow 2-subgroups are rational groups. Structure of rational groups have been studied extensively, but the general classification of rational groups has not been able to be done up to now. In this paper, we show that a full symmetric group of prime degree does not have any rational transitive proper subgroup and that a rational doubly transitive permutation group containing a full cycle is the full symmetric group. We also obtain several results related to the study of rational groups. (C) 2013 Mathematical Institute Slovak Academy of Sciences
URI
http://hdl.handle.net/20.500.12627/143367
https://doi.org/10.2478/s12175-013-0167-5
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Creative Commons Lisansı

İstanbul Üniversitesi Akademik Arşiv Sistemi (ilgili içerikte aksi belirtilmediği sürece) Creative Commons Alıntı-GayriTicari-Türetilemez 4.0 Uluslararası Lisansı ile lisanslanmıştır.

DSpace software copyright © 2002-2016  DuraSpace
Contact Us | Send Feedback
Theme by 
Atmire NV