کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6414849 1630516 2014 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Regular and p-regular orbits of solvable linear groups
ترجمه فارسی عنوان
مدار منظم و منظم گروه های خطی قابل حل است
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

Let V be a faithful G-module for a finite group G and let p be a prime dividing |G|. An orbit vG for the action of G on V is p-regular if |vG|p=|G:CG(v)|p=|G|p. Zhang asks the following question in Zhang (1993) [8]. Assume that a finite solvable group G acts faithfully and irreducibly on a vector space V over a finite field F. If G has a p-regular orbit for every prime p dividing |G|, is it true that G will have a regular orbit on V? In Lü and Cao (2000) [4], Lü and Cao construct an example showing that the answer to this question is no, however the example itself is not correct. In this paper, we study Zhangʼs question in detail. We construct examples showing that the answer to this question is no in general. We also prove the following result. Assume a finite solvable group G of odd order acts faithfully and irreducibly on a vector space V over a field of odd characteristic. If G has a p-regular orbit for every prime p dividing |G|, then G will have a regular orbit on V.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 398, 15 January 2014, Pages 509-518
نویسندگان
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