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arXiv · 1709.08745

The Replacement Property of PSL$(2,p)$ and PSL$(2,p^2)$

Hy P. G Lam
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Abstract

In 2014, Benjamin Nachman showed that when $p\equiv$1 mod 8, the 2-dimensional projective linear group over the field of $p$ elements fails the replacement property if the maximal length $m$ of an irredundant generating sequence for the group is 3. In addition, if $m=4$, the group satisfies the property for any prime $p$. In this paper, we will extend such classification for PSL$(2,q)$ where $q$ is $p$ and $p^2$ with conditions of modulo 8 and 10 on $p$.

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Hy P. G Lam. 2017-09-25. The Replacement Property of PSL$(2,p)$ and PSL$(2,p^2)$. https://arxiv.org/abs/1709.08745

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