群定律与群簇

Group Law and Varieties

中文关键词:  字  标准指数  簇.

英文关键词:word  standard exponent  variety.

中文摘要:

      对于任意字, 文献[1] 引入了概念: 字的标准幂指数.设$\omega_1$和$\omega_2$是两个齐次字, 并假定它们分别定义群簇$V_{\omega_1}$ 与$V_{\omega_2}$.若用$\theta_{\omega_i}$表示$\omega_i$的标准幂指数,则我们有: 若$V_{\omega_1}\subseteq V_{\omega_2}$, 则 $\theta_{\omega_1} | \ \theta_{\omega_2}$.

英文摘要:

      Let $\omega_1$ and $\omega_2$ be two homogeneous words and suppose that they respectively define the varieties $V_{\omega_1}$ and $V_{\omega_2}$ of groups. Denote by $\theta_{\omega_i}$ the standard exponent of $\omega_i$ for $i=1,2$, which was introduced in Ref.\,[1]. We obtain that if $V_{\omega_1}\subseteq V_{\omega_2}$, then $\theta_{\omega_1} | \theta_{\omega_2}$.