Group Law and Varieties |
Received:April 14, 2005 Revised:July 13, 2007 |
Key Words:
word standard exponent variety.
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Fund Project:the Scientific Research Foundation for the Returned Oversears Chinese Scholars, Shanxi Province. |
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Abstract: |
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 $\theta_{\omega_1} | \theta_{\omega_2}$. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2008.01.016 |
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