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出 处:《沈阳工程学院学报(自然科学版)》2010年第4期381-382,共2页Journal of Shenyang Institute of Engineering:Natural Science
基 金:辽宁省教育厅科技基金资助项目(No.2008516)
摘 要:对一个正整数n,若所有共轭数长度都与其互素的有限群均可解.则称n为共轭类可解互素数,简记为CSC-数;类似地,将此定义中的"共轭数长度"替换为"不可约复特征标次数",则称n为特征标次数可解互素数,简记为DSC-数.同时证明了,正整数n是CSC-数(DSC-数)的充要条件是n能被2或15整除.The positive integer n is called conjugation class of solvable coprime number(abbreviated CSC-number) if all the conjugation class lengths and their coprime finite group are solvable;similarly,if "conjugation class lengths" of the definition is replaced by "irreducible complex character degrees",then n is called the solvable coprime number of irreducible complex character degrees(abbreviated DSC-number).In this paper,it is proved that n being divided exactly by 2 or 15 is the necessary and sufficient condition for n being a CSC-number(DSC-number).
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