Group Law and Varieties
Received:April 14, 2005  Revised:July 13, 2007
Key Words: word   standard exponent   variety.  
Fund Project:the Scientific Research Foundation for the Returned Oversears Chinese Scholars, Shanxi Province.
Author NameAffiliation
LI Qian-lu Department of Mathematics, Shanxi Datong University, Shanxi 037009, China 
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      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 $\theta_{\omega_1} | \theta_{\omega_2}$.
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