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On nilpotent groups and conjugacy classes | | Edith Adan-Bante
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1 Aug 2005 | | Subject: | Group Theory MSC-class: 20d15 | math.GR | | Abstract: | Let $G$ be a nilpotent group and $ain G$. Let $a^G={g^{-1}agmid gin G}$ be the conjugacy class of $a$ in $G$. Assume that $a^G$ and $b^G$ are conjugacy classes of $G$ with the property that $|a^G|=|b^G|=p$, where $p$ is an odd prime number. Set $a^G b^G={xymid xin a^G, yin b^G}$. Then either $a^G b^G=(ab)^G$ or $a^G b^G$ is the union of at least $frac{p+1}{2}$ distinct conjugacy classes. As an application of the previous result, given any nilpotent group $G$ and any conjugacy class $a^G$ of size $p$, we describe the square $a^G a^G$ of $a^G$ in terms of conjugacy classes of $G$. | | Source: | arXiv, math.GR/0508048 | | Services: | Forum | Review | PDF | Favorites | |
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